Content-Type: multipart/mixed; boundary="-------------0203140610700" This is a multi-part message in MIME format. ---------------0203140610700 Content-Type: text/plain; name="02-121.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="02-121.keywords" Random Schroedinger Operators ---------------0203140610700 Content-Type: application/postscript; name="oamp-proc.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="oamp-proc.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: oamp-proc.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -N0 -f oamp-proc.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.03.14:1259 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/copypage{}N/p 3 def @MacSetUp}N/doclip{ psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N/@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}N/@setspecial{ CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR }{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N/copypage{}N newpath}N /@endspecial{count ocount sub{pop}repeat countdictstack dcount sub{end} repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N /@fedspecial{end}B/li{lineto}B/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X /yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginProcSet: color.pro %! TeXDict begin/setcmykcolor where{pop}{/setcmykcolor{dup 10 eq{pop setrgbcolor}{1 sub 4 1 roll 3{3 index add neg dup 0 lt{pop 0}if 3 1 roll }repeat setrgbcolor pop}ifelse}B}ifelse/TeXcolorcmyk{setcmykcolor}def /TeXcolorrgb{setrgbcolor}def/TeXcolorgrey{setgray}def/TeXcolorgray{ setgray}def/TeXcolorhsb{sethsbcolor}def/currentcmykcolor where{pop}{ /currentcmykcolor{currentrgbcolor 10}B}ifelse/DC{exch dup userdict exch known{pop pop}{X}ifelse}B/GreenYellow{0.15 0 0.69 0 setcmykcolor}DC /Yellow{0 0 1 0 setcmykcolor}DC/Goldenrod{0 0.10 0.84 0 setcmykcolor}DC /Dandelion{0 0.29 0.84 0 setcmykcolor}DC/Apricot{0 0.32 0.52 0 setcmykcolor}DC/Peach{0 0.50 0.70 0 setcmykcolor}DC/Melon{0 0.46 0.50 0 setcmykcolor}DC/YellowOrange{0 0.42 1 0 setcmykcolor}DC/Orange{0 0.61 0.87 0 setcmykcolor}DC/BurntOrange{0 0.51 1 0 setcmykcolor}DC /Bittersweet{0 0.75 1 0.24 setcmykcolor}DC/RedOrange{0 0.77 0.87 0 setcmykcolor}DC/Mahogany{0 0.85 0.87 0.35 setcmykcolor}DC/Maroon{0 0.87 0.68 0.32 setcmykcolor}DC/BrickRed{0 0.89 0.94 0.28 setcmykcolor}DC/Red{ 0 1 1 0 setcmykcolor}DC/OrangeRed{0 1 0.50 0 setcmykcolor}DC/RubineRed{ 0 1 0.13 0 setcmykcolor}DC/WildStrawberry{0 0.96 0.39 0 setcmykcolor}DC /Salmon{0 0.53 0.38 0 setcmykcolor}DC/CarnationPink{0 0.63 0 0 setcmykcolor}DC/Magenta{0 1 0 0 setcmykcolor}DC/VioletRed{0 0.81 0 0 setcmykcolor}DC/Rhodamine{0 0.82 0 0 setcmykcolor}DC/Mulberry{0.34 0.90 0 0.02 setcmykcolor}DC/RedViolet{0.07 0.90 0 0.34 setcmykcolor}DC /Fuchsia{0.47 0.91 0 0.08 setcmykcolor}DC/Lavender{0 0.48 0 0 setcmykcolor}DC/Thistle{0.12 0.59 0 0 setcmykcolor}DC/Orchid{0.32 0.64 0 0 setcmykcolor}DC/DarkOrchid{0.40 0.80 0.20 0 setcmykcolor}DC/Purple{ 0.45 0.86 0 0 setcmykcolor}DC/Plum{0.50 1 0 0 setcmykcolor}DC/Violet{ 0.79 0.88 0 0 setcmykcolor}DC/RoyalPurple{0.75 0.90 0 0 setcmykcolor}DC /BlueViolet{0.86 0.91 0 0.04 setcmykcolor}DC/Periwinkle{0.57 0.55 0 0 setcmykcolor}DC/CadetBlue{0.62 0.57 0.23 0 setcmykcolor}DC /CornflowerBlue{0.65 0.13 0 0 setcmykcolor}DC/MidnightBlue{0.98 0.13 0 0.43 setcmykcolor}DC/NavyBlue{0.94 0.54 0 0 setcmykcolor}DC/RoyalBlue{1 0.50 0 0 setcmykcolor}DC/Blue{1 1 0 0 setcmykcolor}DC/Cerulean{0.94 0.11 0 0 setcmykcolor}DC/Cyan{1 0 0 0 setcmykcolor}DC/ProcessBlue{0.96 0 0 0 setcmykcolor}DC/SkyBlue{0.62 0 0.12 0 setcmykcolor}DC/Turquoise{0.85 0 0.20 0 setcmykcolor}DC/TealBlue{0.86 0 0.34 0.02 setcmykcolor}DC /Aquamarine{0.82 0 0.30 0 setcmykcolor}DC/BlueGreen{0.85 0 0.33 0 setcmykcolor}DC/Emerald{1 0 0.50 0 setcmykcolor}DC/JungleGreen{0.99 0 0.52 0 setcmykcolor}DC/SeaGreen{0.69 0 0.50 0 setcmykcolor}DC/Green{1 0 1 0 setcmykcolor}DC/ForestGreen{0.91 0 0.88 0.12 setcmykcolor}DC /PineGreen{0.92 0 0.59 0.25 setcmykcolor}DC/LimeGreen{0.50 0 1 0 setcmykcolor}DC/YellowGreen{0.44 0 0.74 0 setcmykcolor}DC/SpringGreen{ 0.26 0 0.76 0 setcmykcolor}DC/OliveGreen{0.64 0 0.95 0.40 setcmykcolor} DC/RawSienna{0 0.72 1 0.45 setcmykcolor}DC/Sepia{0 0.83 1 0.70 setcmykcolor}DC/Brown{0 0.81 1 0.60 setcmykcolor}DC/Tan{0.14 0.42 0.56 0 setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (oamp-proc.dvi) @start %DVIPSBitmapFont: Fa cmmi6 6 1 /Fa 1 34 df<150E0002141F12065A001C140F121848140714C0D8600113061303A39038 07800C00E0141CEC001815386C48137039701F81E0007FB5FC01FB13C0D83FF31380391F E1FE00380F80F820177E9527>33 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb cmsy6 6 1 /Fb 1 49 df48 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc cmti10 10.95 43 /Fc 43 123 df11 D<933807FF80043F13E09338FE00F8DB01F0133EDB07E0130E4B48131F4C137F031F14FF 4BC7FCA218FE157E1878180015FE5DA31401A25DA414030103B712F0A218E0903A0003F0 00070207140F4B14C0A3171F020F15805DA2173F1800141F5D5F177EA2143F92C712FE5F A34A1301027EECF81CA3160302FEECF03C4A1538A21878187013014A010113F018E09338 00F1C0EF7F804948EC1F0094C7FCA35C1307A2001E5B127F130F00FF5BA249CAFC12FEEA F81EEA703CEA7878EA1FF0EA07C0385383BF33>I<14031580A2EC01C0EC00E0A21570A2 15781538153CA3151EA4151FA2150FA7151FA9153FA2153EA3157EA2157CA215FCA215F8 A21401A215F0A2140315E0A2140715C0A2EC0F80A2141F15005C143EA25CA25CA2495A5C 1303495A5C130F49C7FC131E5B137C5B5B485A485A485A48C8FC121E5A12705A5A205A7F C325>41 D44 D<387FFFFEA3B5FCA21705799521>I<120FEA3FC0127FA212FFA31380EA7F00123C0A0A 77891C>I<1838187CA218F8170118F0EF03E0A2EF07C0A2EF0F80171F1800173EA25FA2 5F16015F4C5AA24C5AA24C5A161F94C7FC163EA25EA25E15015E4B5AA24B5AA24B5A151F 93C8FC153EA25DA25D14015D4A5AA24A5AA24A5A141F92C9FC143EA25CA25C13015C495A A2495AA2495A131F91CAFC133EA25BA25B12015B485AA2485AA2485A121F90CBFC123EA2 5AA25AA25A5A365B7FC32E>I<15FE913807FF8091381F07C091387C01F0ECF000494813 F8494813780107147C495A49C7FC167E133E137EA25BA2485AA2000315FEA25B000715FC A2491301120FA34848EB03F8A44848EB07F0A448C7EA0FE0A316C0007E141F12FE168015 3FA2481500A2157EA25DA25D4813015D6C495A127C4A5A4A5A6C49C7FC143E6C5B380FC1 F03803FFC0C648C8FC273F76BC2E>I<15031507150F151F151E153E157EEC01FEEC03FC 1407141FEB01FF90380FFBF8EB1FC3EB0E07130015F0A2140FA215E0A2141FA215C0A214 3FA21580A2147FA21500A25CA25CA21301A25CA21303A25CA21307A25CA2130FA25CA213 1FA25CEB7FE0B612F0A215E0203D77BC2E>I<15FE913803FFC091380F01F091383C00F8 4A137C4A7F4948133F49487F4A148049C7FC5BEB0E0C011E15C0EB1C0EEB3C0613381378 1370020E133FD9F00C148013E0141C0218137F00011600EBC0384A13FEEC600102E05B3A 00E3C003F89039FF0007F0013C495A90C7485A5E037FC7FC15FC4A5A4A5AEC0FC04AC8FC 147E14F8EB03E0495A011FC9FC133E49141801F0143C48481438485A1678485A48C85A12 0E001E4A5AD83FE0130301FF495A397C3FF01FD8780FB55AD8700391C7FCD8F0015B486C 6C5A6E5AEC07C02A3F79BC2E>I<131EEB3F80137FEBFFC05AA214806C13005B133C90C7 FCB3120FEA3FC0127FA212FFA35B6CC7FC123C122777A61C>58 D<171C173C177CA217FC A216011603A21607A24C7EA2161DA216391679167116E1A2ED01C1A2ED03811507160115 0EA2031C7FA24B7EA25D15F05D4A5AA24A5AA24AC7FC5C140E5C021FB6FC4A81A20270C7 127FA25C13015C495AA249C8FCA2130E131E131C133C5B01F882487ED807FEEC01FFB500 E0017FEBFF80A25C39417BC044>65 D<49B812F8A390260003FEC7121F18074B14031801 F000F014075DA3140F5D19E0A2141F4B1338A2EF7801023F027013C04B91C7FCA217F002 7F5CED80011603160F91B65AA3ED001F49EC07805CA3010392C8FC5CF003804C13070107 020E14005C93C75A180E010F161E4A151C183CA2011F5E5C60A2013F15014A4A5A170701 7F150F4D5A4A147F01FF913807FF80B9FCA295C7FC3D3E7BBD3E>69 D<49B812F0A390260003FEC7123F180F4B1403A2F001E014075DA3140F5D19C0A2141F5D 1770EFF003023F02E013804B91C7FCA21601027F5CED8003A2160702FFEB1F8092B5FCA3 49D9003FC8FC4A7F82A20103140E5CA2161E0107141C5CA293C9FC130F5CA3131F5CA313 3F5CA2137FA25C497EB612E0A33C3E7BBD3B>I<49B648B6FC495DA2D9000390C7000313 004B5D4B5DA2180714074B5DA2180F140F4B5DA2181F141F4B5DA2183F143F4B5DA2187F 147F4B5DA218FF91B8FC96C7FCA292C712015B4A5DA2170313034A5DA2170713074A5DA2 170F130F4A5DA2171F131F4A5DA2173F133F4A5DA2017F157FA24A5D496C4A7EB66CB67E A3483E7BBD44>72 D<49B612C0A25FD9000390C8FC5D5DA314075DA3140F5DA3141F5DA3 143F5DA3147F5DA314FF92C9FCA35B5CA313035C18C0EF01E0010716C05C17031880130F 4A140718005F131F4A141EA2173E013F5D4A14FC1601017F4A5A16074A131F01FFECFFF0 B8FCA25F333E7BBD39>76 D81 D<92390FF001C0ED7FFE4AB5EA0380913907F80FC791390FC003EF91391F8001FF4A C71300027E805C495A4948143EA2495AA2010F153C5CA3011F1538A38094C7FC80A214FC 6DB4FC15F015FE6DEBFFC06D14F06D14FC6D80143F020F7F020180EC001F150303007F16 7F163FA2161FA212075A5F120EA2001E153F94C7FCA2163E003E157E167C003F15FC4B5A 486C5C4B5A6D495AD87DE0EB1F80D8F8F849C8FC017F13FE39F03FFFF8D8E00F13E048C6 90C9FC32427ABF33>83 D<48B9FCA25A903AFE001FF00101F89138E0007FD807E0163E49 013F141E5B48C75BA2001E147FA2001C4B131C123C003814FFA2007892C7FC12704A153C 00F01738485CC716001403A25DA21407A25DA2140FA25DA2141FA25DA2143FA25DA2147F A25DA214FFA292C9FCA25BA25CA21303A25CEB0FFE003FB67E5AA2383D71BC41>I<147E 49B47E903907C1C38090391F80EFC090383F00FF017E137F4914804848133F485AA24848 1400120F5B001F5C157E485AA215FE007F5C90C7FCA21401485C5AA21403EDF0385AA214 07EDE078020F1370127C021F13F0007E013F13E0003E137FECF3E1261F01E313C03A0F87 81E3803A03FF00FF00D800FC133E252977A72E>97 DIIII<167C4BB4FC923807C78092380F83C0ED1F 87161FED3F3FA2157EA21780EE0E004BC7FCA414015DA414035DA30103B512F8A3902600 07E0C7FCA3140F5DA5141F5DA4143F92C8FCA45C147EA414FE5CA413015CA4495AA4495A A4495A121E127F5C12FF49C9FCA2EAFE1EEAF83C1270EA7878EA3FE0EA0F802A5383BF1C >III<1478EB01 FCA21303A314F8EB00E01400AD137C48B4FC38038F80EA0707000E13C0121E121CEA3C0F 1238A2EA781F00701380A2EAF03F140012005B137E13FE5BA212015BA212035B14381207 13E0000F1378EBC070A214F0EB80E0A2EB81C01383148038078700EA03FEEA00F8163E79 BC1C>I 107 DIIII<903903E001F890390FF807FE903A1E7C1E0F80903A1C3E 3C07C0013C137801389038E003E0EB783F017001C013F0ED80019038F07F0001E015F814 7E1603000113FEA2C75AA20101140717F05CA20103140F17E05CA20107EC1FC0A24A1480 163F010F15005E167E5E131F4B5A6E485A4B5A90393FB80F80DA9C1FC7FCEC0FFCEC03E0 49C9FCA2137EA213FEA25BA21201A25BA21203A2387FFFE0B5FCA22D3A80A72E>I114 DII<137C48B4141C26038F 80137EEA0707000E7F001E15FE121CD83C0F5C12381501EA781F007001805BA2D8F03F13 03140000005D5B017E1307A201FE5C5B150F1201495CA2151F0003EDC1C0491481A2153F 1683EE0380A2ED7F07000102FF13005C01F8EBDF0F00009038079F0E90397C0F0F1C9039 1FFC07F8903907F001F02A2979A731>I<017CEB01C048B4EB07F038038F80EA0707000E 01C013F8121E001C1403EA3C0F0038EC01F0A2D8781F130000705BA2EAF03F91C712E012 005B017E130116C013FE5B1503000115805BA2ED07001203495B150EA25DA25D15780001 14706D5B0000495A6D485AD97E0FC7FCEB1FFEEB03F0252979A72A>I<017C167048B491 387001FC3A038F8001F8EA0707000E01C015FE001E1403001CEDF000EA3C0F0038177C15 07D8781F4A133C00701380A2D8F03F130F020049133812005B017E011F14784C137013FE 5B033F14F0000192C712E05BA2170100034A14C049137E17031880A2EF070015FE170E00 010101141E01F86D131C0000D9039F5BD9FC076D5A903A3E0F07C1E0903A1FFC03FFC090 2703F0007FC7FC372979A73C>I<903903F001F890390FFC07FE90393C1E0E0F9026780F 1C138001F0EBB83FD801E013F89039C007F07FEA0380000714E0D9000F140048151C000E 4AC7FCA2001E131FA2C75BA2143F92C8FCA35C147EA314FE4A131CA30101143C001E1538 003F491378D87F811470018314F000FF5D9039077801C039FE0F7C033A7C0E3C07802778 3C1E1EC7FC391FF80FFC3907E003F029297CA72A>I<137C48B4143826038F8013FCEA07 07000E7F001E1401001C15F8EA3C0F12381503D8781F14F000701380A2D8F03F13070200 13E012005B017E130F16C013FE5B151F1201491480A2153F000315005BA25D157EA315FE 5D00011301EBF8030000130790387C1FF8EB3FF9EB07E1EB00035DA21407000E5CEA3F80 007F495AA24A5AD8FF0090C7FC143E007C137E00705B387801F0383803E0381E0FC06CB4 C8FCEA03F8263B79A72C>II E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmr12 12 16 /Fd 16 118 df<143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E007F B6FCA3204278C131>49 DI<49B4FC01 0F13E0013F13FC9038FE01FE3A01F0007F80D803C0EB3FC048C7EA1FE0120EED0FF0EA0F E0486C14F8A215077F5BA26C48130FEA03C0C813F0A3ED1FE0A2ED3FC01680ED7F0015FE 4A5AEC03F0EC1FC0D90FFFC7FC15F090380001FCEC007FED3F80ED1FC0ED0FE016F0ED07 F816FC150316FEA2150116FFA3121EEA7F80487EA416FE491303A2007EC713FC00701407 003015F80038140F6C15F06CEC1FE06C6CEB3FC0D803E0EB7F803A01FE01FE0039007FFF F8010F13E0010190C7FC28447CC131>II<000615C0D807C0130701FCEB7F80 90B612005D5D5D15E0158026063FFCC7FC90C9FCAE14FF010713C090381F01F090383800 FC01F0137ED807C07F49EB1F8016C090C7120F000615E0C8EA07F0A316F81503A216FCA5 123E127F487EA416F890C712075A006015F0A20070140F003015E00038EC1FC07E001EEC 3F806CEC7F006C6C13FE6C6C485A3901F807F039007FFFE0011F90C7FCEB07F826447BC1 31>II<121CA2EA1F8090B712C0A3481680A217005E 0038C8120C0030151C00705D0060153016705E5E4814014B5A4BC7FCC81206150E5D1518 15385D156015E04A5AA24A5A140792C8FC5CA25C141E143EA2147E147CA214FCA21301A3 495AA41307A6130FAA6D5AEB01C02A457BC231>I<14FF010713E0011F13F890387F00FE 01FC133FD801F0EB1F804848EB0FC049EB07E00007EC03F048481301A290C713F8481400 A47FA26D130116F07F6C6CEB03E013FC6C6CEB07C09039FF800F806C9038C01F006CEBF0 3EECF87839007FFEF090383FFFC07F01077F6D13F8497F90381E7FFFD97C1F1380496C13 C02601E00313E048486C13F000079038007FF84848EB3FFC48C7120F003EEC07FE150148 140016FF167F48153FA2161FA56C151E007C153EA2007E153C003E157C6C15F86DEB01F0 6C6CEB03E06C6CEB07C0D803F8EB1F80C6B4EBFF0090383FFFFC010F13F0010113802844 7CC131>I<14FF010713E0011F13F890387F80FC9038FC007E48487F4848EB1F804848EB 0FC0000FEC07E0485AED03F0485A16F8007F140190C713FCA25AA216FE1500A516FFA46C 5CA36C7E5D121F7F000F5C6C6C1306150E6C6C5B6C6C5BD8007C5B90383F01E090390FFF 80FE903801FE0090C8FC150116FCA4ED03F8A216F0D80F801307486C14E0486C130F16C0 ED1F80A249EB3F0049137E001EC75A001C495A000F495A3907E01FE06CB51280C649C7FC EB1FF028447CC131>I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121EEA7F80 A2EAFFC0A4EA7F80A2EA1E000A2B78AA1B>I70 D101 D103 D105 D<3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C000015B13FBEC007E153C 01FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>114 D117 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmr10 10 14 /Fe 14 117 df<121C127FEAFF80A5EA7F00121C0909798817>46 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E7FEC0C1FA2021C7FEC18 0FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F81A249C77F167FA20106 810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA213E0707E1201486C81D8 0FFC02071380B56C90B512FEA3373C7DBB3E>65 D<013FB512E0A39039001FFC00EC07F8 B3B3A3123FEA7F80EAFFC0A44A5A1380D87F005B0070131F6C5C6C495A6C49C7FC380781 FC3801FFF038007F80233B7DB82B>74 D79 D<003FB812E0A3D9C003EB001F273E0001 FE130348EE01F00078160000701770A300601730A400E01738481718A4C71600B3B09138 07FF80011FB612E0A335397DB83C>84 D99 DII<147E903803FF8090380FC1E0 EB1F8790383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E 387FFFF8A31C3B7FBA19>I104 D111 D<3903F01FE000FFEB7FF89038F1E07E9039F3801F 803A07F7000FC0D803FEEB07E049EB03F04914F849130116FC150016FEA3167FAA16FEA3 ED01FCA26DEB03F816F06D13076DEB0FE001F614C09039F7803F009038F1E07E9038F0FF F8EC1FC091C8FCAB487EB512C0A328357EA42E>I<3807E01F00FFEB7FC09038E1E3E090 38E387F0380FE707EA03E613EE9038EC03E09038FC0080491300A45BB3A2487EB512F0A3 1C257EA421>114 D<1318A51338A31378A313F8120112031207001FB5FCB6FCA2D801F8 C7FCB215C0A93800FC011580EB7C03017E13006D5AEB0FFEEB01F81A347FB220>116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmsy7 7 1 /Ff 1 4 df<1338A50060130C00F8133E00FC137E00FE13FE383FBBF83807FFC0000113 00EA007C48B4FC000713C0383FBBF838FE38FE00FC137E00F8133E0060130C00001300A5 17197B9A22>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmbx12 17.28 26 /Fg 26 120 df<16F04B7E1507151F153FEC01FF1407147F010FB5FCB7FCA41487EBF007 C7FCB3B3B3B3007FB91280A6395E74DD51>49 D<913801FFF8021FEBFFC091B612F80103 15FF010F16C0013F8290267FFC0114F89027FFE0003F7F4890C7000F7F48486E7FD807F8 6E148048486E14C048486E14E048486F13F001FC17F8486C816D17FC6E80B56C16FE8380 A219FFA283A36C5BA26C5B6C90C8FCD807FC5DEA01F0CA14FEA34D13FCA219F85F19F04D 13E0A294B512C019804C14004C5B604C5B4C5B604C13804C90C7FC4C5A4C5A4B13F05F4B 13804B90C8FC4B5AED1FF84B5A4B5A4B48143F4A5B4A48C8FC4A5A4A48157E4A5A4A5AEC 7F8092C9FC02FE16FE495A495A4948ED01FCD90FC0150749B8FC5B5B90B9FC5A4818F85A 5A5A5A5ABAFCA219F0A4405E78DD51>I<92B5FC020F14F8023F14FF49B712C04916F001 0FD9C01F13FC90271FFC00077FD93FE001017F49486D8049C86C7F484883486C6F7F14C0 486D826E806E82487FA4805CA36C5E4A5E6C5B6C5B6C495E011FC85A90C95CA294B55A61 4C91C7FC604C5B4C5B4C5B4C5B047F138092260FFFFEC8FC020FB512F817E094C9FC17F8 17FF91C7003F13E0040713F8040113FE707F717F7113E085717FA2717F85A285831A80A3 1AC0EA03FCEA0FFF487F487F487FA2B57EA31A80A34D14005C7E4A5E5F6C495E49C8485B D81FF85F000F5ED807FE92B55A6C6C6C4914806C01F0010791C7FC6C9026FF803F5B6D90 B65A011F16F0010716C001014BC8FCD9001F14F0020149C9FC426079DD51>I65 D73 D77 D82 D<001FBEFCA64849C79126E0000F148002E018 0091C8171F498601F81A0349864986A2491B7FA2491B3F007F1DC090C9181FA4007E1C0F A600FE1DE0481C07A5CA95C7FCB3B3B3A3021FBAFCA663617AE070>84 D<913803FFFE027FEBFFF00103B612FE010F6F7E4916E090273FFE001F7FD97FE001077F D9FFF801017F486D6D7F717E486D6E7F85717FA2717FA36C496E7FA26C5B6D5AEB1FC090 C9FCA74BB6FC157F0207B7FC147F49B61207010F14C0013FEBFE004913F048B512C04891 C7FC485B4813F85A5C485B5A5CA2B55AA45FA25F806C5E806C047D7F6EEB01F96C6DD903 F1EBFF806C01FED90FE114FF6C9027FFC07FC01580000191B5487E6C6C4B7E011F02FC13 0F010302F001011400D9001F90CBFC49437CC14E>97 D<92380FFFF04AB67E020F15F002 3F15FC91B77E01039039FE001FFF4901F8010113804901E0010713C04901804913E0017F 90C7FC49484A13F0A2485B485B5A5C5A7113E0485B7113C048701380943800FE0095C7FC 485BA4B5FCAE7EA280A27EA2806C18FCA26C6D150119F87E6C6D15036EED07F06C18E06C 6D150F6D6DEC1FC06D01E0EC7F806D6DECFF00010701FCEB03FE6D9039FFC03FFC010091 B512F0023F5D020F1580020102FCC7FCDA000F13C03E437BC148>99 DI< 92380FFFC04AB512FC020FECFF80023F15E091B712F80103D9FE037F499039F0007FFF01 1F01C0011F7F49496D7F4990C76C7F49486E7F48498048844A804884485B727E5A5C4871 7EA35A5C721380A2B5FCA391B9FCA41A0002C0CBFCA67EA380A27EA27E6E160FF11F806C 183F6C7FF17F006C7F6C6D16FE6C17016D6C4B5A6D6D4A5A6D01E04A5A6D6DEC3FE00103 01FC49B45A6D9026FFC01F90C7FC6D6C90B55A021F15F8020715E0020092C8FC030713F0 41437CC14A>III<903807FF80B6FCA6C6FC7F7FB3A8EF1FFF94B5 12F0040714FC041F14FF4C8193267FE07F7F922781FE001F7FDB83F86D7FDB87F07FDB8F C0814C7F039FC78015BE03BC8003FC825DA25DA25DA45DB3B2B7D8F007B71280A651647B E35A>II<90 3807FF80B6FCA6C6FC7F7FB3A90503B61280A6DD003FEB8000DE0FFCC7FCF01FF04E5AF0 FFC04D5B4D90C8FCEF07FC4D5AEF3FF04D5A4D5A4C90C9FC4C5AEE0FFC4C5A4C5AEE7FC0 4C7E03837F03877F158F039F7F03BF7F92B5FC838403FC804B7E03F0804B6C7F4B6C7F15 80707F707F707FA270807080717FA2717F717F717FA2717F717F83867180727F95B57EB7 D8E00FECFFF0A64C647BE355>107 D<903807FF80B6FCA6C6FC7F7FB3B3B3B3ADB712E0 A623647BE32C>I<902607FF80D91FFFEEFFF8B691B500F00207EBFF80040702FC023F14 E0041F02FF91B612F84C6F488193267FE07F6D4801037F922781FE001F9027E00FF0007F C6DA83F86D9026F01FC06D7F6DD987F06D4A487F6DD98FC0DBF87EC7804C6D027C80039F C76E488203BEEEFDF003BC6E4A8003FC04FF834B5FA24B5FA24B94C8FCA44B5EB3B2B7D8 F007B7D8803FB612FCA67E417BC087>I<902607FF80EB1FFFB691B512F0040714FC041F 14FF4C8193267FE07F7F922781FE001F7FC6DA83F86D7F6DD987F07F6DD98FC0814C7F03 9FC78015BE03BC8003FC825DA25DA25DA45DB3B2B7D8F007B71280A651417BC05A>I<92 3807FFE092B6FC020715E0021F15F8027F15FE494848C66C6C7E010701F0010F13E04901 C001037F49496D7F4990C87F49486F7E49486F7E48496F13804819C04A814819E048496F 13F0A24819F8A348496F13FCA34819FEA4B518FFAD6C19FEA46C6D4B13FCA36C19F8A26C 6D4B13F0A26C19E06C6D4B13C0A26C6D4B13806C6D4B13006D6C4B5A6D6D495B6D6D495B 010701F0010F13E06D01FE017F5B010090B7C7FC023F15FC020715E0020092C8FC030713 E048437CC151>I114 D<913A3FFF8007800107 B5EAF81F011FECFE7F017F91B5FC48B8FC48EBE0014890C7121FD80FFC1407D81FF08016 00485A007F167F49153FA212FF171FA27F7F7F6D92C7FC13FF14E014FF6C14F8EDFFC06C 15FC16FF6C16C06C16F06C826C826C826C82013F1680010F16C01303D9007F15E0020315 F0EC001F1500041F13F81607007C150100FC81177F6C163FA2171F7EA26D16F0A27F173F 6D16E06D157F6D16C001FEEDFF806D0203130002C0EB0FFE02FCEB7FFC01DFB65A010F5D D8FE0315C026F8007F49C7FC48010F13E035437BC140>II<902607FFC0ED3FFEB60207B5FCA6C6EE00 076D826D82B3B3A260A360A2607F60183E6D6D147E4E7F6D6D4948806D6DD907F0ECFF80 6D01FFEB3FE06D91B55A6E1500021F5C020314F8DA003F018002F0C7FC51427BC05A>I< B70081B600FC0103B512FCA6C66C0180C701FCC8381FFE006F6FED03F86D047F5F856F6E 16076D646F70140F6D705F866F6E161F6D646F4A6D143F6D99C7FC4E7F6F616D1B7E6F4A 6D14FE6D6395B57E7001FC15016E62DCC0016E13036EDBF87F5D05038004E0496C14076E 62DCF007ED800F6E4B6C5D050F15C004F8496C141F6E62DCFC1FEDE03F6E4B6C92C8FC05 3F15F004FE496C5C6E197E7048EDF8FE6E027E6D5C05FE15FC4D6D13FD6F601BFF6F496E 5BA24D806F60A26F496E5BA24D806F60A26F496E90C9FCA294C87E6F5FA26F486F5A047C 6F5A6E417DBF75>119 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh cmr6 6 2 /Fh 2 51 df<13E01201120712FF12F91201B3A7487EB512C0A212217AA01E>49 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmsy8 8 5 /Fi 5 113 df0 D<12E012F812FEEA3F80EA0FE0EA03F8EA00FE EB3F80EB0FE0EB03F8EB00FC143FEC0FC0EC07F0EC01FCEC007FED1FC0ED07F0ED01FCED 007FEE1FC01607161FEE7F00ED01FCED07F0ED1FC0037FC7FCEC01FCEC07F0EC0FC0023F C8FC14FCEB03F8EB0FE0EB3F8001FEC9FCEA03F8EA0FE0EA3F80007ECAFC12F812E0CBFC AD007FB71280B812C0A22A3B7AAB37>21 D<137813FE1201A3120313FCA3EA07F8A313F0 A2EA0FE0A313C0121F1380A3EA3F00A3123E127E127CA35AA35A0F227EA413>48 D<91B512C01307131FD97F80C7FC01FCC8FCEA01F0EA03C0485A48C9FC120E121E5A1238 12781270A212F05AA3B712C0A300E0C9FCA37E1270A212781238123C7E120E120F6C7E6C 7EEA01F0EA00FCEB7F80011FB512C013071300222B7AA52F>50 D<18031807180F180E18 1E181C183C18381878187018F018E01701EF03C01880170718005F170E171E171C173C17 381778177017F05F16015F16035F160701C092C7FC486C5C0007151E486C141C003F153C D873F8143800E31578D801FC147016F06C6C5C1501017F5C1503D93F805B1507D91FC090 C8FC5D90380FE00E151E903807F01C153C903803F83815786D6C5A5DEB00FF5D147F5D14 3F92C9FC80141E140E38427C823B>112 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmex10 10.95 12 /Fj 12 106 df<140E141E143C147814F01301EB03E0EB07C0A2EB0F80EB1F00A2133E13 7E137C13FC5B1201A2485AA3485AA2120F5BA2121FA25BA2123FA390C7FCA25AA6127E12 FEB3A4127E127FA67EA27FA3121FA27FA2120FA27F1207A26C7EA36C7EA212007F137C13 7E133E7FA2EB0F80EB07C0A2EB03E0EB01F013001478143C141E140E176C72832A>0 D<12E07E12787E7E121F6C7E6C7EA26C7E6C7EA26C7E7F137C137E133E133FA2EB1F80A3 EB0FC0A214E01307A214F0A21303A214F8A31301A214FCA6130014FEB3A414FC1301A614 F8A21303A314F0A21307A214E0A2130F14C0A2EB1F80A3EB3F00A2133E137E137C13FC5B 485AA2485A485AA2485A48C7FC121E5A5A5A5A176C7C832A>II I<150F157FEC01FFEC07FCEC1FE0EC7FC0ECFF00495A5C13035C13075CB3AD130F5C131F 5C495A49C7FCEA01FEEA03F8EA0FF0EA7F8000FEC8FCA2EA7F80EA0FF0EA03F8EA01FEEA 007F6D7E6D7E80130F801307B3AD801303801301806D7EEC7FC0EC1FE0EC07FCEC01FFEC 007F150F206C768335>8 D<12F012FEEAFFC0EA1FF0EA07FCEA01FE6C6C7EEB3FC0131F 80130F801307B3AD8013038013016D7E147FEC3F80EC1FE0EC07F8EC01FEEC007FA2EC01 FEEC07F8EC1FE0EC3F80EC7F0014FE495A13035C13075CB3AD130F5C131F5C133FEBFF80 4848C7FCEA07FCEA1FF0EAFFC048C8FC12F0206C768335>I16 D<12F07E127C7E7E6C7E6C7E7F6C7E6C7E12007F137E7FA26D7E6D7EA26D7EA26D7E6D7E A26D7EA280147E147F80A26E7EA281140FA281140781A21403A281A2140181A3140081A4 157E157FA5811680A9ED1FC0B3A9ED3F80A916005DA5157E15FEA45D1401A35D1403A25D A21407A25D140F5DA2141F5DA24AC7FCA25C147E14FE5CA2495AA2495A495AA2495AA249 5A49C8FCA2137E5B5B1201485A485A5B485A48C9FC123E5A5A5A22A37D8336>I<007C18 1FA200FEF03F80B3B3B3A86C187FA26C19006D5FA2003F606D1601A26C6C4C5A6D160700 0F606D160F6C6C4C5A6C6C4C5A6C6C6CEDFFC06E5C6C01F002075B6D6C4A90C7FC6DB4EC 7FFE6D9039F007FFFC010790B612F06D5E010016806E92C8FC020F14F8020114C0912600 1FFCC9FC415B7B7F4C>83 D88 D104 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmsy10 10.95 22 /Fk 22 113 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fl msbm10 10.95 5 /Fl 5 91 df<007FB612FCB812C06C16F83B01E007C1F7FC3B00F00F00787ED9700EEB38 0F93383C078093381E03C093380E01E01700160F7013F01870A618F018E0A2EE0F019338 0E03C0EF078093381E0F00EE3C3E4C5A923801F3F892380FFFE0020FB5FC17FC17FF913A 0E00FE3F8093381F07C093380781E093380380F0EFC0780401133C181EEFE00E1600180F 1807A6180F180E1601EFC01E183C04031378EF80F093380783E093380F0FC0D9F00F9038 3E7F803C01E007C0FFFE00007FB712F8B812C06C03F8C7FC383E7FBD29>66 D78 D<007FB612F8B87E6C16F02703E007C013FC000090390F003CFE020EEB1C1F93381E0780 93380E03C0EF01E01700040F13F070137018781838A8187818704C13F0040E13E01701EF 03C093381E078093381C1F00EE3C7EEE7BFC020FB512F017C04CC7FC020EC9FCB3A60003 EB0F80007FB512FEB6FC7E353E7FBD37>80 D<007FB612FCB812C06C16F83B03E007C07F FE0000903A0F001F7F80020E9038078FC093380383E0EFC0F0040113788484EFE00E1600 180F84A760180E0401131EEFC01C183C04035BEF81F093380787E093381F7FC04BB5C7FC 020FB512FC17C004F7C8FC91390E1C078092381E03C0ED0E01030F7FED078003037FEEC0 78923801E0380300133C707EEE780EEE380F93383C0780EE1E03040E7F93380F01E09338 0780F004031370EFC078706C7E04007F717E943878078094383803C00003D90F8090383C 01E0007FB500FE90381FFFFCB6806C823E3E7EBD39>82 D<0003B812F05AA2903B0FFC00 1C01E0D93FC0013C13C0D80F7EC7EA7803D80EF802701380D80FE0ECF00749903901E00F 0049ECC00E90C70003131E4C5A001E0207133892380F0078001C020E1370031E13F04B48 5AC800385BED780303705BEDF0074A4848C7FCEDC00E0203131E4A485AED00384A137802 0E1370021E13F04A485A02385BEC7803913870078002F090C8FC49485AECC00E0103131E 49485AEC0038491378010E01701406011E01F0140E49485A01385BD97803151E49485A01 E090C8FC000149153CEBC00E0003011E157C48484815FCEB00384801781401000E49EC03 DC001E49EC0F9CD83C01ED1F3C003849EC7E38D87803EC01F8484848EB1FF0B912F8A337 3E7DBD41>90 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmr8 8 11 /Fm 11 112 df<1406140FA34A7EA34A7EA3EC6FE01467A2ECC7F014C3A290380183F814 8101037F1400A2497F0106137EA249137F81A24980151FA24980150FA249801507A24980 1503000181491301A2000381A2487ED81FE0497ED8FFF890383FFFF0A22C2F7EAE31>3 D<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA0F00A2121EA35AA45A A512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113E0EA00F01370133813 1C130E1307130310437AB11B>40 D<12C07E12707E7E7E120FEA0780120313C0EA01E0A2 EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133CA41378A313F0A2EA01 E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>III<140EA2141E143EA2147E14FEA2EB01BE130314 3E1306130E130C131813381330136013E013C0EA0180120313001206120E120C5A123812 305A12E0B612FCA2C7EA3E00A9147F90381FFFFCA21E2D7EAC23>I<013F13F89038FFC3 FE3903E1FF1E3807807C000F140C391F003E00A2003E7FA76C133EA26C6C5A0007137838 0FE1F0380CFFC0D81C3FC7FC90C8FCA3121E121F380FFFF814FF6C14C04814F0391E0007 F848130048147C12F848143CA46C147C007C14F86CEB01F06CEB03E03907E01F803901FF FE0038003FF01F2D7E9D23>103 D108 D111 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmmi8 8 27 /Fn 27 122 df11 D<157E913801FFC091380781E091381E00F01438 4A13F84A1378495A494813F891C7FC5B1306010E1301010C14F0131C0118EB03E0ED07C0 013814809039301FEF00EC3FFE13709038601FEF9138000F80ED07C013E04914E0A31201 5BA30003140F90C713C0A348EC1F80A2ED3F00A2486C137E000D147C6D5B390CE001F039 1C7003E039183C0F80D91FFEC7FCEB03F80038C9FC1230A312701260A312E05AA3253C7E AE28>I<131FD9FFC013304801F0137000076D13604815E0D9807C13C0391E003C014801 1E13800038EB0E03480107130000605CEC030612E0C7138EEC018C159C159815B815B0A2 15F05DA35DA25DA21403A44AC7FCA4140EA45CA31418242C7F9D24>I<147C49B4FC9038 03C78090380783C090381F03E0EB1E01133E017C13F013F8A2EA01F0120313E01207A2EA 0FC01403A2EA1F80A21407003F14E0130090B5FCA2397F000FC0127EA2141F1580127C00 FC14005CA2147EA248137C14FC00785B495AA2387C03E0383C07C0495A001C90C7FCEA1E 3EEA0FF8EA03E01C307DAE21>18 D<13E0486C133C15FF00031303EC0F7F9038E01C7EEC 381C000749C7FC5CEBC3C001C7C8FCEA0FDE13F8EBFF8014F8381F83FEEB803F496C7E14 0F48154016C0123EA2007E14811680007C1403ED830000FC1487EC078E48EB03FC0070EB 00F0221F7D9D29>20 D<131C013EEB0380ED07C0017E130F1680137CA201FC131F16005B A200015C153E5BA20003147E157C5BA20007ECFC08EDF8185BA2000F0101133816309038 E003F002071370001F90380EF8609039F83C78E090397FF03FC090391FC00F0048C9FCA2 123EA2127EA2127CA212FCA25AA21270252C7E9D2A>22 DI<90B612F812035A4815F03A1E0380C000003C130000701301130700E05CEAC0063800 0E03A3131CA2133C140713381378A201F07FA21201A2D803E07FA20007130313C0A26C48 6C5A251E7E9C29>25 D<160E486C143F120348C813801206000E151F000C150F001C1600 00188112380030130C141E007015061260143E023C130E00E0150C5A0238131C6C01785B 14705E02F013F06C486C485A010313033A7C0FFC0FC03A7FFFBFFF80023F90C7FC393FFC 1FFE391FF80FF83907E007E0291F7F9D2C>33 DI<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A5A12600915 7A8714>59 D<013FB6FC17C0903A00FE0007F0EE01F84AEB00FC177E1301177F5CA21303 177E4A14FEA20107EC01FC17F84AEB03F0EE07E0010FEC1FC0EE7F009138C003FC91B55A 4914FE9139C0003F804AEB0FC017E0013F140717F091C7FC16035BA2017E1407A201FE15 E0160F4915C0161F0001ED3F80EE7F004914FEED03F80003EC0FF0B712C003FCC7FC302D 7CAC35>66 D<013FB71280A2D900FEC7127F170F4A1407A20101150318005CA21303A25C 16300107147094C7FC4A136016E0130F15019138C007C091B5FC5BECC0074A6C5AA2133F A20200EB000CA249151C92C71218017E1538173001FE15705F5B4C5A000115034C5A4914 0F161F00034AB4C7FCB8FC5E312D7DAC34>69 D<90273FFFFC0FB5FCA2D900FEC7EA3F80 A24A1500A201015D177E5CA2010315FE5F5CA2010714015F5CA2010F14035F5C91B6FC5B 9139C00007E05CA2013F140F5F91C7FCA249141F5F137EA201FE143F94C7FC5BA200015D 167E5BA2000315FEB539E03FFFF8A2382D7CAC3A>72 D<90383FFFFEA2010090C8FC5C5C A21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C7EA0180A249 14031700017E5C160601FE140EA2495C163C12015E49EB01F84B5A0003141FB7FC5E292D 7DAC30>76 D96 D<13F8121FA21201A25BA21203A25BA21207 A25BA2120FEBC7E0EB9FF8EBB83C381FF01EEBE01F13C09038800F80EA3F00A2123EA200 7E131FA2127CA2143F00FC14005AA2147EA2147C14FC5C387801F01303495A383C0F806C 48C7FCEA0FFCEA03F0192F7DAD1E>98 D101 D<1307EB0F80EB1FC0A2EB0F80EB070090C7FCA9EA01E0EA07F8 EA0E3CEA1C3E123812301270EA607EEAE07C12C013FC485A120012015B12035BA21207EB C04014C0120F13801381381F01801303EB0700EA0F06131EEA07F8EA01F0122E7EAC18> 105 D<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA2120115F89038F003FC EC0F0E0003EB1C1EEC387EEBE07014E03807E1C09038E3803849C7FC13CEEA0FDC13F8A2 EBFF80381F9FE0EB83F0EB01F81300481404150C123EA2007E141C1518007CEBF038ECF8 3000FC1470EC78E048EB3FC00070EB0F801F2F7DAD25>107 D<27078007F0137E3C1FE0 1FFC03FF803C18F0781F0783E03B3878E00F1E01263079C001B87F26707F8013B0006001 0013F001FE14E000E015C0485A4914800081021F130300015F491400A200034A13076049 133E170F0007027EEC8080188149017C131F1801000F02FCEB3F03053E130049495C180E 001F0101EC1E0C183C010049EB0FF0000E6D48EB03E0391F7E9D3E>109 D<3907C007E0391FE03FF83918F8783E393879E01E39307B801F38707F00126013FEEAE0 FC12C05B00815C0001143E5BA20003147E157C5B15FC0007ECF8081618EBC00115F0000F 1538913803E0300180147016E0001F010113C015E390C7EAFF00000E143E251F7E9D2B> I<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C0000713F000069038E0 03E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C0133EA2017EEB1F80A2 017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FFC7FCEBF0FC000390 C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>112 D<3807C01F390FF07FC039 1CF8E0E0383879C138307B8738707F07EA607E13FC00E0EB03804848C7FCA2128112015B A21203A25BA21207A25BA2120FA25BA2121FA290C8FC120E1B1F7E9D20>114 DI<013F137C9038FFC1FF3A01C1 E383803A0380F703C0390700F60F000E13FE4813FC12180038EC0700003049C7FCA2EA20 0100005BA313035CA301075B5D14C000385CD87C0F130600FC140E011F130C011B131C39 F03BE038D8707113F0393FE0FFC0260F803FC7FC221F7E9D28>120 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmmi10 10.95 46 /Fo 46 123 df11 D13 DII<15FCEC03FF91380F87C09138 3E03E0EC7C0102F813F01301903903F000F8495A010F14FC5C495A133F91C7FC4914FE13 FEA212015B12034913011207A25B000F15FC1503121F5BA21507003F15F890B6FCA33A7F C0000FF05BA2151F16E048C7FCA2ED3FC0A2481580157F1600A215FEA24A5AA24A5A007E 5C14075D4A5A003E5C141F4AC7FC6C137E5C380F81F03807C3E03801FF80D8007EC8FC27 417DBF2B>18 D<131C013E141F017EEC7FC0ED01FFED07BF01FEEB1E3F03381380491370 9238E01E0000014948C7FCEC0780D9F80EC8FC5C00035B14F0EBF3C001FFC9FC4813F0EC FF809038E07FF0EC07FC000FEB00FE157F496D7EA2001F141F17705BA2003F16F0033F13 E090C71300A248ED01C0A2007EEC1F03178000FE91380F0700168E48EC07FC0038EC01F0 2C297CA734>20 D22 D<017FEC01C0D83FFFEC03E016075B 1200160F17C05B161F00011680163F491500A20003157EA2495C150100075D4B5A49495A A2000F4A5A4B5A4949C7FC157E001F147C5D49485AEC07E0003F495A4AC8FCEB003E14F8 48485AEB07C0D87E1FC9FC13FCEAFFE0138000F8CAFC2B287CA72D>I<020FB512FE027F 14FF49B7FC1307011F15FE903A3FE03FE00090387F000F01FE6D7E484813034848804848 1301485A5B121F5B123F90C7FC5A127EA2150300FE5D5AA24B5AA2150F5E4B5AA2007C4A C7FC157E157C6C5C001E495A001FEB07E0390F800F802603E07EC8FC3800FFF8EB3FC030 287DA634>27 D32 D<18E00130ED03F80170ED07FC13F0485A5B12034915030007160148CAFC187C120E121E 001C173C003C021C14380038147EA20078177803FE147000705CA218F04A4814E000F016 01A24BEB03C0A24BEB07800203140F6C0107EC1F00173E6CD91FF0137E007C013F5C007E 90397FF803F83B7F83FFFE1FF0263FFFFCB5FC4A14C06C496C5B6C01C091C7FC6C903800 1FFCD801FCEB07E036297FA739>II<121EEA 7F80A2EAFFC0A4EA7F80A2EA1E000A0A798919>58 D<121EEA7F8012FF13C0A213E0A312 7FEA1E601200A413E013C0A312011380120313005A120E5A1218123812300B1C798919> I<180E183F18FFEF03FEEF0FF8EF3FE0EFFF80933803FE00EE0FF8EE3FE0EEFF80DB03FE C7FCED1FF8ED7FE0913801FF80DA07FEC8FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7F C04848CAFCEA07FCEA1FF0EA7FC048CBFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1F F0EB07FCEB01FF9038007FC0EC1FF0EC07FE913801FF809138007FE0ED1FF8ED03FE9238 00FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FEEF00FF183F180E383679 B147>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF90 38007FC0EC1FF8EC07FE913801FF809138007FE0ED0FF8ED03FE923800FF80EE3FE0EE0F F8EE03FE933800FF80EF3FE0EF0FF8EF03FEEF00FFA2EF03FEEF0FF8EF3FE0EFFF809338 03FE00EE0FF8EE3FE0EEFF80DB03FEC7FCED0FF8ED7FE0913801FF80DA07FEC8FCEC1FF8 EC7FC04948C9FCEB07FCEB1FF0EB7FC04848CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270 383679B147>62 D<15FF020713E091381F00F80278133E4A7F4948EB0F804948EB07C049 48EB03E091C7FC496CEB01F002E014F8131F160017FCA25C0107C812FE90C9FCA7EC03FC EC3FFF9138FE03C1903903F000E149481371D91F80133149C7123B017EEC1BFC5B000115 1F4848140F484815F8A2485A121F17F0485A161F17E0127F5BEE3FC0A200FF168090C812 7F1700A216FEA2484A5A5E007E1403007F4A5A5E6C4A5A6C6C495A4BC7FC6C6C13FE6C6C 485A3903F80FF06CB512C06C6C90C8FCEB0FF82F437CC030>64 D<17075F84171FA2173F 177FA217FFA25E5EA24C6C7EA2EE0E3F161E161C1638A21670A216E0ED01C084ED038017 1FED07005D150E5DA25D157815705D844A5A170F4A5A4AC7FC92B6FC5CA2021CC7120F14 3C14384A81A24A140713015C495AA249C8FC5B130E131E4982137C13FED807FFED1FFEB5 00F00107B512FCA219F83E417DC044>I<49B712F818FF19E090260001FEC7EA3FF0F007 F84B6E7E727E850203815D1A80A20207167F4B15FFA3020F17004B5C611803021F5E4B4A 5A180FF01FE0023F4B5A4B4A5ADD01FEC7FCEF07F8027FEC7FE092B6C8FC18E092C7EA07 F84AEC01FE4A6E7E727E727E13014A82181FA213034A82A301075F4A153FA261010F167F 4A5E18FF4D90C7FC011F5E4A14034D5A013FED1FF04D5A4AECFFC0017F020790C8FCB812 FC17F094C9FC413E7DBD45>II< 49B912C0A3D9000190C71201F0003F4B151F190F1A80020316075DA314075D1A00A2140F 4BEB0380A205075B021FED000E4B92C7FC5FA2023F141E5D173EEE01FE4AB55AA3ED8001 02FF6D5A92C71278A34915705C191C05F0133C01034B13384A167894C71270A2010717F0 4A5E180161010F16034A4B5AA2180F011F4CC7FC4A5D187E013F16FE4D5A4A140F017F15 FFB95AA260423E7DBD43>69 D71 D<49B6D8C03FB512F81BF01780D900010180C7383FF00093C85B4B 5EA2197F14034B5EA219FF14074B93C7FCA260140F4B5DA21803141F4B5DA21807143F4B 5DA2180F4AB7FC61A20380C7121F14FF92C85BA2183F5B4A5EA2187F13034A5EA218FF13 074A93C8FCA25F130F4A5DA21703131F4A5DA2013F1507A24A5D496C4A7EB6D8E01FB512 FCA2614D3E7DBD4C>I<92B612E0A39239003FF000161F5FA2163F5FA3167F5FA316FF94 C7FCA35D5EA315035EA315075EA3150F5EA3151FA25EA2153FA25EA2157FA25EA2D80F80 13FFEA3FC0486C91C8FCA25CD8FFC05B140301805B49485A00FC5C0070495A0078495A00 38495A001E017EC9FC380F81FC3803FFE0C690CAFC33407ABD32>74 D<49B612F0A3D900010180C7FC93C8FC5DA314035DA314075DA3140F5DA3141F5DA3143F 5DA3147F5DA314FF92C9FCA35B5C180C181E0103161C5C183C183813074A1578187018F0 130F4AEC01E0A21703011FED07C04A140F171F013FED3F8017FF4A1303017F021F1300B9 FCA25F373E7DBD3E>76 D<49B712F018FF19C0D9000190C76C7EF00FF84BEC03FC180102 0382727E5DA214071A805DA2140F4E13005DA2021F5E18034B5D1807023F5E4E5A4B4A5A 4E5A027F4B5A06FEC7FC4BEB03FCEF3FF091B712C005FCC8FC92CBFCA25BA25CA21303A2 5CA21307A25CA2130FA25CA2131FA25CA2133FA25C497EB612E0A3413E7DBD3A>80 D<49B77E18F818FFD90001D900017F9438003FE04BEC0FF0727E727E14034B6E7EA30207 825DA3020F4B5A5DA24E5A141F4B4A5A614E5A023F4B5A4B4A5A06FEC7FCEF03FC027FEC 0FF04BEBFF8092B500FCC8FC5F9139FF8001FE92C7EA7F80EF1FC084496F7E4A1407A284 13035CA2170F13075C60171F130F5CA3011F033F5B4AEE038018E0013F17071A004A021F 5B496C160EB600E090380FF01E05075B716C5ACBEAFFE0F03F8041407DBD45>82 D<007FB500F090387FFFFE19FC5D26007FE0C7000313804A913800FC004A5D187001FF16 F0A291C95AA2481601605BA200031603605BA20007160795C7FC5BA2000F5E170E5BA200 1F161E171C5BA2003F163C17385BA2007F1678A2491570A200FF16F0A290C95AA216015F 5A16035F16074CC8FC160E161E5E007F5D5E6C4A5A6D495A6C6C495A6C6C011FC9FC6C6C 137E3903FC03F8C6B512E0013F1380D907FCCAFC3F407ABD3E>85 DI<027FB5D88007B512C091B6 FCA2020101F8C7EBF8009126007FE0EC7F804C92C7FC033F157C701478616F6C495A4E5A 6F6C495A4EC8FC180E6F6C5B606F6C5B6017016F6C485A4D5A6F018FC9FC179E17BCEE7F F85F705AA3707EA283163F167FEEF7FCED01E7EEC3FEED0383ED070392380E01FF151E4B 6C7F5D5D4A486D7E4A5A4A486D7E92C7FC140E4A6E7E5C4A6E7E14F0495A49486E7E1307 D91F806E7ED97FC014072603FFE0EC1FFF007F01FC49B512FEB55CA24A3E7EBD4B>88 D<151EED7F80913801F1C0EC03C1EC07C0ED80E0EC0F005C141E91383E01C0147CA214F8 1503D901F01380A21303ECE007010714005D90380FC00EA2151E90381F801C153C5D133F 4A5A5D140149485A017E5B14074AC7FCEBFE1E13FC5C5C5C3801F9E0EBFBC0A2EBFF8091 C8FC5B5B5B5BA212031207120F121F123D127800F0140300E0EC0780C66CEB0F00017813 1E157C6D13F04A5A90381E0F80D90FFEC7FCEB03F823417FBF26>96 D99 DII104 D<143C14FEA21301A314FCEB00701400AD137E3801FF803803C7C0EA0703000F13E0120E 121C13071238A2EA780F007013C0A2EAF01F14801200133F14005B137EA213FE5BA21201 5B0003130E13F0A20007131EEBE01CA2143CEBC0381478147014E013C13803E3C03801FF 00EA007C173E7EBC1F>I107 D109 DI112 D114 DI<017E147848B4EB01FC2603C7C013FED807 031303000F13E0120E121C0107130100381400167ED8780F143E00705B161EEAF01F4A13 1C1200133F91C7123C16385B137E167801FE14705B16F016E0120149EB01C0A2ED0380A2 ED0700A20000140E5D6D133C017C5B6D5B90381F03C0903807FF80D901FCC7FC27297EA7 2C>118 D120 D<137C48B4EC03802603C7C0EB0FC0EA0703000F7F000E 151F001C168013071238163FD8780F150000705BA2D8F01F5C4A137E1200133F91C712FE 5E5B137E150113FE495CA2150300015D5BA215075EA2150F151F00005D6D133F017C137F 017E13FF90393F03DF8090380FFF1FEB01FC90C7123F93C7FCA25DD80380137ED80FE013 FE001F5C4A5AA24848485A4A5A6CC6485A001C495A001E49C8FC000E137C380781F03803 FFC0C648C9FC2A3B7EA72D>I<02F8130ED903FE131ED90FFF131C49EB803C49EBC07849 14F090397E07F1E09038F800FF49EB1FC049EB07800001EC0F006C48131E90C75A5D5D4A 5A4A5A4A5A4AC7FC143E14785C495A495A495A49C8FC011E14E05B5B4913014848EB03C0 485AD807F8EB078048B4131F3A1F87E07F00391E03FFFE486C5B00785CD870005B00F0EB 7FC048011FC7FC27297DA72A>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmr10 10.95 88 /Fp 88 128 df0 D<16E04B7EA24B7EA24B7EA24B7EA2 ED1DFFA203387FA29238787FC015709238F03FE015E002016D7E15C002036D7E15800207 6D7E15004A6D7E140E021E6D7E141C023C6D7F143802786E7E147002F06E7E5C01016F7E 5C01036F7E5C01076F7E91C8FC496F7E130E011E6F7E131C013C6F7F13380178707E1370 01F0707E5B0001717E5B0003717E5B0007717E90CAFC48717E120E001E717E001FBAFC48 1980A24819C0A2BB12E0A243417CC04C>I<153CA3157EA315FFA34A7FA34A7FA215BFA2 9138073FE0151FA2020E7F150FA2021C7F1507A2023C7FEC3803A202787F14701501A202 E07F81A2494880167FA2494880163FA201078191C7121FA24981010E140FA2011E81131C 1607A249811603A249811601A201F081821201486C4A1380D80FFE020713C0B500E090B6 FCA338417DC03F>3 D6 D<913801FFC0021F13FC 9139FF007F80D903F8EB0FE0D90FF0EB07F8D91FC0EB01FCD97F806DB4FC49C86C7E4848 6F7E00038348486F7E000F8349150F001F83491507003F83A348486F7EAA6C6C4B5AA300 1F5FA26C6C4B5AA200075F6D151F00035FA26C6C4B5A00005FA2017F4BC7FC6D157EA26D 6C5C010F5DA26D6C495A00E0EF0380010315E0D870019238C007006E130301001580A36C 0160EC000E003C017049131E263FFFF0ECFFFEA36C5FA339407CBF42>10 D<4AB4EB0FE0021F9038E03FFC913A7F00F8FC1ED901FC90383FF03FD907F090397FE07F 80494801FF13FF4948485BD93F805C137F0200ED7F00EF003E01FE6D91C7FC82ADB97EA3 C648C76CC8FCB3AE486C4A7E007FD9FC3FEBFF80A339407FBF35>I<4AB4FC021F13C091 387F01F0903901FC0078D907F0131C4948133E494813FF49485A137F1400A213FE6F5A16 3893C7FCAA167FB8FCA33900FE00018182B3AC486CECFF80007FD9FC3F13FEA32F407FBF 33>I<4AB47E021F13F791387F00FFEB01F8903807F001EB0FE0EB1FC0EB3F80137F1400 8101FE80AEB8FCA3C648C77EB3AE486CECFF80007FD9FC3F13FEA32F407FBF33>I<127C 12FC7E7EA2EA7F80EA3FC0EA1FE0120FEA07F0EA03F81201EA007C133E131F130E130410 1176BE2D>18 D<133E133F137F13FFA2EA01FEEA03FCEA07F813F0EA0FE0EA1FC01380EA 3E005A5A1270122010116EBE2D>I22 D<001E130F397F803FC000 FF137F01C013E0A201E013F0A3007F133F391E600F3000001300A401E01370491360A300 0114E04913C00003130101001380481303000EEB070048130E0018130C0038131C003013 181C1C7DBE2D>34 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312 011380120313005A120E5A1218123812300B1C79BE19>39 D<1430147014E0EB01C0EB03 801307EB0F00131E133E133C5B13F85B12015B1203A2485AA2120F5BA2121F90C7FCA25A A3123E127EA6127C12FCB2127C127EA6123E123FA37EA27F120FA27F1207A26C7EA21201 7F12007F13787F133E131E7FEB07801303EB01C0EB00E014701430145A77C323>I<12C0 7E12707E7E121E7E6C7E7F12036C7E7F12007F1378137CA27FA2133F7FA21480130FA214 C0A3130714E0A6130314F0B214E01307A614C0130FA31480A2131F1400A25B133EA25BA2 137813F85B12015B485A12075B48C7FC121E121C5A5A5A5A145A7BC323>I<1506150FB3 A9007FB912E0BA12F0A26C18E0C8000FC9FCB3A915063C3C7BB447>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A 120E5A1218123812300B1C798919>II<121EEA7F80A2EAFFC0A4 EA7F80A2EA1E000A0A798919>I48 DIII<150E15 1E153EA2157EA215FE1401A21403EC077E1406140E141CA214381470A214E0EB01C0A2EB 0380EB0700A2130E5BA25B5BA25B5B1201485A90C7FC5A120E120C121C5AA25A5AB8FCA3 C8EAFE00AC4A7E49B6FCA3283E7EBD2D>I<00061403D80780131F01F813FE90B5FC5D5D 5D15C092C7FC14FCEB3FE090C9FCACEB01FE90380FFF8090383E03E090387001F8496C7E 49137E497F90C713800006141FC813C0A216E0150FA316F0A3120C127F7F12FFA416E090 C7121F12FC007015C012780038EC3F80123C6CEC7F00001F14FE6C6C485A6C6C485A3903 F80FE0C6B55A013F90C7FCEB07F8243F7CBC2D>II<1238123C123F90B612FCA316F85A16F016E00078C712010070EC03C0ED 078016005D48141E151C153C5DC8127015F04A5A5D14034A5A92C7FC5C141EA25CA2147C 147814F8A213015C1303A31307A3130F5CA2131FA6133FAA6D5A0107C8FC26407BBD2D> III<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3121E EA7F80A2EAFFC0A4EA7F80A2EA1E000A2779A619>I<121EEA7F80A2EAFFC0A4EA7F80A2 EA1E00C7FCB3121E127FEAFF80A213C0A4127F121E1200A412011380A3120313005A1206 120E120C121C5A1230A20A3979A619>I<007FB912E0BA12F0A26C18E0CDFCAE007FB912 E0BA12F0A26C18E03C167BA147>61 D<15074B7EA34B7EA34B7EA34B7EA34B7E15E7A291 3801C7FC15C3A291380381FEA34AC67EA3020E6D7EA34A6D7EA34A6D7EA34A6D7EA34A6D 7EA349486D7E91B6FCA249819138800001A249C87EA24982010E157FA2011E82011C153F A2013C820138151FA2017882170F13FC00034C7ED80FFF4B7EB500F0010FB512F8A33D41 7DC044>65 DI IIIIIII<011FB512FCA3D9000713006E5A1401B3 B3A6123FEA7F80EAFFC0A44A5A1380D87F005B007C130700385C003C495A6C495A6C495A 2603E07EC7FC3800FFF8EB3FC026407CBD2F>IIIIIIIIII<003FB912 80A3903AF0007FE001018090393FC0003F48C7ED1FC0007E1707127C00781703A3007017 01A548EF00E0A5C81600B3B14B7E4B7E0107B612FEA33B3D7DBC42>II II89 D<003FB712F8A391C7EA1F F013F801E0EC3FE00180EC7FC090C8FC003EEDFF80A2003C4A1300007C4A5A12784B5A4B 5AA200704A5AA24B5A4B5AA2C8485A4A90C7FCA24A5A4A5AA24A5AA24A5A4A5AA24A5A4A 5AA24990C8FCA2495A4948141CA2495A495AA2495A495A173C495AA24890C8FC485A1778 485A484815F8A24848140116034848140F4848143FED01FFB8FCA32E3E7BBD38>II<486C13C00003130101001380481303 000EEB070048130E0018130C0038131C003013180070133800601330A300E01370481360 A400CFEB678039FFC07FE001E013F0A3007F133FA2003F131F01C013E0390F0007801C1C 73BE2D>II<1318133C137E13FF38 01E7803803C3C0380781E0380F00F0001E137848133C48131E48130F00601306180D76BD 2D>I97 DI<49B4FC010F13E090383F00F8017C131E4848131F4848137F0007ECFF80485A5B12 1FA24848EB7F00151C007F91C7FCA290C9FC5AAB6C7EA3003FEC01C07F001F140316806C 6C13076C6C14000003140E6C6C131E6C6C137890383F01F090380FFFC0D901FEC7FC222A 7DA828>IIII<167C903903F801FF903A1FFF078F8090397E0FDE 1F9038F803F83803F001A23B07E000FC0600000F6EC7FC49137E001F147FA8000F147E6D 13FE00075C6C6C485AA23901F803E03903FE0FC026071FFFC8FCEB03F80006CAFC120EA3 120FA27F7F6CB512E015FE6C6E7E6C15E06C810003813A0FC0001FFC48C7EA01FE003E14 0048157E825A82A46C5D007C153E007E157E6C5D6C6C495A6C6C495AD803F0EB0FC0D800 FE017FC7FC90383FFFFC010313C0293D7EA82D>III<1478EB01 FEA2EB03FFA4EB01FEA2EB00781400AC147FEB7FFFA313017F147FB3B3A5123E127F38FF 807E14FEA214FCEB81F8EA7F01387C03F0381E07C0380FFF803801FC00185185BD1C>I< EA01FC12FFA3120712031201B292B51280A392383FFC0016E0168093C7FC153C5D5D4A5A EC07C04A5A4AC8FC143E147F4A7E13FD9038FFDFC0EC9FE0140F496C7E01FC7F496C7E14 01816E7E81826F7E151F826F7EA282486C14FEB539F07FFFE0A32B3F7EBE30>II<2701F801FE14FF00FF9027 07FFC00313E0913B1E07E00F03F0913B7803F03C01F80007903BE001F87000FC2603F9C0 6D487F000101805C01FBD900FF147F91C75B13FF4992C7FCA2495CB3A6486C496CECFF80 B5D8F87FD9FC3F13FEA347287DA74C>I<3901F801FE00FF903807FFC091381E07E09138 7803F000079038E001F82603F9C07F0001138001FB6D7E91C7FC13FF5BA25BB3A6486C49 7EB5D8F87F13FCA32E287DA733>I<14FF010713E090381F81F890387E007E01F8131F48 48EB0F804848EB07C04848EB03E0000F15F04848EB01F8A2003F15FCA248C812FEA44815 FFA96C15FEA36C6CEB01FCA3001F15F86C6CEB03F0A26C6CEB07E06C6CEB0FC06C6CEB1F 80D8007EEB7E0090383F81FC90380FFFF0010090C7FC282A7EA82D>I<3901FC03FC00FF 90381FFF8091387C0FE09039FDE003F03A03FFC001FC6C496C7E91C7127F49EC3F805BEE 1FC017E0A2EE0FF0A3EE07F8AAEE0FF0A4EE1FE0A2EE3FC06D1580EE7F007F6E13FE9138 C001F89039FDE007F09039FC780FC0DA3FFFC7FCEC07F891C9FCAD487EB512F8A32D3A7E A733>I<02FF131C0107EBC03C90381F80F090397F00387C01FC131CD803F8130E4848EB 0FFC150748481303121F485A1501485AA448C7FCAA6C7EA36C7EA2001F14036C7E15076C 6C130F6C7E6C6C133DD8007E137990383F81F190380FFFC1903801FE0190C7FCAD4B7E92 B512F8A32D3A7DA730>I<3901F807E000FFEB1FF8EC787CECE1FE3807F9C100031381EA 01FB1401EC00FC01FF1330491300A35BB3A5487EB512FEA31F287EA724>I<90383FC060 3901FFF8E03807C03F381F000F003E1307003C1303127C0078130112F81400A27E7E7E6D 1300EA7FF8EBFFC06C13F86C13FE6C7F6C1480000114C0D8003F13E0010313F0EB001FEC 0FF800E01303A214017E1400A27E15F07E14016C14E06CEB03C0903880078039F3E01F00 38E0FFFC38C01FE01D2A7DA824>I<131CA6133CA4137CA213FCA2120112031207001FB5 12C0B6FCA2D801FCC7FCB3A215E0A912009038FE01C0A2EB7F03013F138090381F8700EB 07FEEB01F81B397EB723>IIIII< B539E00FFFE0A32707FE000313006C48EB01FC6F5A00015D7F00005DA2017F495AA2EC80 03013F5CA26D6C48C7FCA26E5A010F130EA26D6C5AA2ECF83C01031338A26D6C5AA2ECFE F001005BA2EC7FC0A36E5AA36EC8FCA2140EA2141E141C143C1438A2147800181370127E B45BA2495AA248485AD87E07C9FCEA780EEA3C3CEA1FF8EA07E02B3A7EA630>I<001FB6 1280A2EBE0000180140049485A001E495A121C4A5A003C495A141F00385C4A5A147F5D4A C7FCC6485AA2495A495A130F5C495A90393FC00380A2EB7F80EBFF005A5B484813071207 491400485A48485BA248485B4848137F00FF495A90B6FCA221277EA628>I<001C130E00 7FEB3F8039FF807FC0A5397F003F80001CEB0E001A0977BD2D>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq cmbx10 10.95 26 /Fq 26 122 df46 D48 D<140F143F5C495A130F48B5 FCB6FCA313F7EAFE071200B3B3A8B712F0A5243C78BB34>I<903803FF80013F13F890B5 12FE00036E7E4881260FF80F7F261FC0037F4848C67F486C6D7E6D6D7E487E6D6D7EA26F 1380A46C5A6C5A6C5A0007C7FCC8FC4B1300A25E153F5E4B5AA24B5A5E4A5B4A5B4A48C7 FC5D4A5AEC1FE04A5A4A5A9139FF000F80EB01FC495A4948EB1F00495AEB1F8049C7FC01 7E5C5B48B7FC485D5A5A5A5A5AB7FC5EA4293C7BBB34>I<903801FFE0010F13FE013F6D 7E90B612E04801817F3A03FC007FF8D807F06D7E82D80FFC131F6D80121F7FA56C5A5E6C 48133FD801F05CC8FC4B5A5E4B5A4A5B020F5B902607FFFEC7FC15F815FEEDFFC0D90001 13F06E6C7E6F7E6F7E6F7E1780A26F13C0A217E0EA0FC0487E487E487E487EA317C0A25D 491580127F49491300D83FC0495A6C6C495A3A0FFE01FFF86CB65A6C5DC61580013F49C7 FC010313E02B3D7CBB34>II<00071538D80FE0EB01F801FE133F90B6FC5E5E5E5E93C7FC5D15F85D15C04AC8FC01 80C9FCA9ECFFC0018713FC019F13FF90B67E020113E09039F8007FF0496D7E01C06D7E5B 6CC77FC8120F82A31780A21207EA1FC0487E487E12FF7FA21700A25B4B5A6C5A01805C6C C7123F6D495AD81FE0495A260FFC075B6CB65A6C92C7FCC614FC013F13F0010790C8FC29 3D7BBB34>II<121F7F13F890 B712F0A45A17E017C0178017005E5E5A007EC7EA01F84B5A007C4A5A4B5A4B5A93C7FC48 5C157E5DC7485A4A5AA24A5A140F5D141F143F5D147FA214FF92C8FC5BA25BA3495AA313 0FA5131FAA6D5A6D5A6D5A2C3F7ABD34>II<16FCA24B7EA2 4B7EA34B7FA24B7FA34B7FA24B7FA34B7F157C03FC7FEDF87FA2020180EDF03F0203804B 7E02078115C082020F814B7E021F811500824A81023E7F027E81027C7FA202FC814A147F 49B77EA34982A2D907E0C7001F7F4A80010F835C83011F8391C87E4983133E83017E8301 7C81B500FC91B612FCA5463F7CBE4F>65 D72 D<003FB912FCA5903BFE003FFE003FD87FF0EE0FFE01C0160349160190C71500197E127E A2007C183EA400FC183F48181FA5C81600B3AF010FB712F8A5403D7CBC49>84 D<903807FFC0013F13F848B6FC48812607FE037F260FF8007F6DEB3FF0486C806F7EA36F 7EA26C5A6C5AEA01E0C8FC153F91B5FC130F137F3901FFFE0F4813E0000F1380381FFE00 485A5B485A12FF5BA4151F7F007F143F6D90387BFF806C6C01FB13FE391FFF07F36CEBFF E100031480C6EC003FD91FF890C7FC2F2B7DA933>97 D<13FFB5FCA512077EAFEDFFE002 0713FC021FEBFF80027F80DAFF8113F09139FC003FF802F06D7E4A6D7E4A13074A807013 80A218C082A318E0AA18C0A25E1880A218005E6E5C6E495A6E495A02FCEB7FF0903AFCFF 01FFE0496CB55AD9F01F91C7FCD9E00713FCC7000113C033407DBE3A>II101 D<13FFB5FCA512077EAFED1FF8EDFFFE02036D7E4A80DA0FE07F91381F007F023C805C4A 6D7E5CA25CA35CB3A4B5D8FE0FB512E0A5333F7CBE3A>104 DI< 01FFD91FF8ECFFC0B590B5010713F80203DAC01F13FE4A6E487FDA0FE09026F07F077F91 261F003FEBF8010007013EDAF9F0806C0178ECFBC04A6DB4486C7FA24A92C7FC4A5CA34A 5CB3A4B5D8FE07B5D8F03FEBFF80A551297CA858>109 D111 D<01FFEBFFE0B5000713FC021FEBFF80027F80DAFF8113F091 39FC007FF8000301F06D7E4A6D7E4A130F4A6D7E1880A27013C0A38218E0AA4C13C0A318 805E18005E6E5C6E495A6E495A02FCEBFFF0DAFF035B92B55A029F91C7FC028713FC0281 13C00280C9FCACB512FEA5333B7DA83A>I<3901FE01FE00FF903807FF804A13E04A13F0 EC3F1F91387C3FF8000713F8000313F0EBFFE0A29138C01FF0ED0FE091388007C092C7FC A391C8FCB3A2B6FCA525297DA82B>114 D<90383FFC1E48B512BE000714FE5A381FF00F 383F800148C7FC007E147EA200FE143EA27E7F6D90C7FC13F8EBFFE06C13FF15C06C14F0 6C806C806C806C80C61580131F1300020713C014000078147F00F8143F151F7EA27E1680 6C143F6D140001E013FF9038F803FE90B55A15F0D8F87F13C026E00FFEC7FC222B7DA929 >II121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmr12 14.4 34 /Fr 34 123 df19 D<120FEA3FC0EA7FE012 FF13F0A213F8A3127F123FEA0F381200A513781370A313F013E0A2120113C01203138012 07EA0F00121EA25A5A12300D23768B21>44 DI48 D<14075C5C147F5C1307133F000FB5FCB6FC13 F913C1EAF0011200B3B3B3A7497F010F13E0B712FEA4274F75CE3B>I<000316C001C014 0301F8141F903AFFC003FF8091B612005E5E5E16E016804BC7FC019F13F8018113800180 C9FCB0EC0FF0ECFFFE01836D7E903987F01FE090399F0007F801BE6D7E01F86D7E496D7E 49EC7F805BEE3FC04915E0C9121F17F0A317F8160FA317FCA5120EEA3F80487E12FF7FA2 17F85B161F5B48C813F012700078ED3FE0A26C16C0167F6CEDFF80001F16006C6C495A6C 6C13036C6CEB07F8D801F8EB1FF06CB4EB7FE06DB51280011F49C7FC010713F8010013C0 2E517ACE3B>53 D67 D 69 DI72 DI76 DII80 D83 D<003FBB12C0A449C79038F0000701F06E48130001C0183F48C8EE0FE0007E1907007C19 03A200781901A400701900A500F01AF0481A70A6C91700B3B3AC4C7E030313FC027FB712 E0A44C517CD055>I97 D99 D<17FF4BB5FCA4ED0007160182B3A6EC0FF8EC7FFF49B512E09039 07FC03F090391FE0007C49487F49C7120F01FE80484880485A000781484880A2485AA248 5AA2127FA35B12FFAB127FA27FA2123FA27F121FA26C6C5C00075D7F6C6C5C6C6C5C6C6C 021E7F6D6C017C13E0D91FC049EBFF8090390FF807E00103B512800100495ADA1FF091C7 FC39547CD241>II104 D<1378EA01FE487E487FA66C90C7FC6C5AEA007890C8FCB0EB7F80B5FCA4 1203C6FC137FB3B3A43801FFE0B61280A419507CCF21>I108 D<01FFEB07FCB590383FFF8092B512E0 913901F00FF8913903C007FC000349C66C7EC6010E13016D486D7E5C143002706E7E1460 14E05CA35CB3AD2601FFE0903801FFE0B600C0B612C0A43A347CB341>110 DI113 D<01FFEB1F80B5EB7FF0913801FFF8913803E1FC91380783 FE0003EB0F07C6131EEB7F1C1438143091387003FC91386000F0160014E05CA45CB3AA80 48487EB612F0A427347DB32E>III I119 D121 D<001FB712E0A301FCC7EA7FC001E014FF01804913 8090C714004B5A001E14074B5A485D4B5A153F4B5A00385D15FF4A5B93C7FC4A5A1407C7 485A5D4A5A143F4A5A5D14FF495B92C8FC494814E01307495A5C495A013FEC01C0495A5C 13FF485B91C71203485A12074848140749140F485A003FED3F80484814FF491307B8FCA3 2B337DB234>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmsy10 14.4 1 /Fs 1 4 df<140E141FAA0030ED018000F8ED03E000FE150F6C151F01C0147FD87FE0EC FFC0D83FF8010313803B0FFC0E07FE00D803FFEB1FF8C690388E3FE090393FCE7F809026 0FFFFEC7FC010313F8010013E0EC3F80ECFFE0010313F8010F13FE90393FCE7F809039FF 8E3FE0000390380E1FF8D80FFCEB07FE3B3FF81F03FF80D87FE0010013C0D8FFC0EC7FE0 0100141F48150F00F815030030ED0180C791C7FCAA140E2B3378B73C>3 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmr17 20.74 20 /Ft 20 122 df70 D72 D80 D<943801FFF0053FEBFF804CB612F0040F9038001FFEDC3FF0903801FF80DCFF80903800 3FE0DB03FEC8EA0FF8DB0FF8ED03FE4B486F7EDB7FC09238007FC04B48707E4A90CA6C7E DA07FEEF0FFC4A48717E4A48717E4A48717F4A48717F4A48727E4949727EA24990CC6C7E 4948737E010F874A19074948737E013F884A85017F884A8501FF8848894A1A7F48894A1A 3FA2488991CE121F4889A34848757EA3003F1E80A24987A3007F1EC0A44987A200FF1EE0 B1007F1EC0A26D63A4003F1E80A36D63001F1E00A36C6C515AA36C656E1A3FA26C656E1A 7F6C65A26C6D505AA26D6CDB3FC04A5B013FDCFFF05E6E020301FC5C011F922607C03E93 C7FC6E91270F800F805B010F92261F00035D6D6C021E6D6C495A6D6C4A6D6C495A053814 606D6D0470495A6D6D01786E495A6E6C01704C5A6E6CDC18015B6E6CDC1C0390C8FC6E6C 4D5A6E6C70485A6E6C4D5A0200D98078ED3FE092267FC0384B5ADB3FF06F485A92260FF8 3C4BC9FC922603FE1EEC0FF8922601FF9FEC3FF0923C003FFF8001FF80040FD9C01F1730 040390B5EAFBC0DC003F14830501EBF00394C8FC871F701A01871FF07515E0A27514011E 03747E1E0775EC0FC076131F76133FE17FF0137F9939FC03FF8099B6FC751500A3755C66 87755C755C755C7514800A3F90C7FCF407F86C9A78F87C>I83 D<913803FF80021F13F891B5 12FE903A03FC01FF80903A07E0003FE0D91F80EB0FF8013EC76C7E496E7E01F06E7E4848 6E7F717E4848153F4982D807A06F7E13FC487E6D6F7E80A2717EA46C90C8FC6C5A6C5ACA FCA6EE07FF0303B5FC157F913903FFFE07021F138091387FF800903801FFC0010790C7FC EB1FFCEB3FF0EBFFE0485B485B4890C8FC5B485A485AA2485A1A0E485AA312FF5B170FA4 171FA26D153F007F163B177B6DDBF1FE131C003F16E16C6C14016C6C912603C0FF13386C 6CEC0F806C6C6C903A1F007F80706C6D017CECE1E028007FF803F8EB3FFF011FB500E06D 1380010391C7000713009026003FF8EC01FC474D79CB4F>97 D99 D101 DI<131EEB7F80497E487F487FA66C5B6C5B6D5A 011EC7FC90C8FCB3A7EB01F0EA07FFB5FCA51201EA007F133FA2131FB3B3B3A3497EEBFF FEB612FCA51E727AF12A>105 D108 DIII<02F849B47ED803FF021F13F8B5027F13FE923A01FC01FF80923A07E0003F E0031FC76C7E033EEC0FFCC60278EC03FE013F496E7E90261FF9E06E7FDAFBC0826DB448 6F7E92C96C7E737E5C4A707E864A160786851B80A2851BC0A2851BE0A5F27FF0AEF2FFE0 A54F13C0A34F1380A21B0061626E160F626E161F626E4C5A4F5A6F5EDAFBC015FFDAF9E0 4A5BDAF8F04A48C7FC03784A5A6F4A5A031FEC3FF06F6CEBFFC0922603F80790C8FC0300 B512FC043F13E0DC07FEC9FC93CBFCB3A7497EEB7FFFB77EA54C6C7BCA58>I114 DI<1407A85CA65CA35CA35CA25CA2 5BA25B5B5B5B5B5B48B712FE120FB8FCA3D8000190C9FCB3B3A2EF01C0B0EF03806D7FA3 027FEC0700815F6E6C130E021F141E6F131C6E6C5B6E6C13F8913901FF01F09139007FFF C0031F5BDB03FCC7FC326B7EE93D>I<02F8EE0F80D803FFEE3FFFB5030FB5FCA5C6EE00 0F013F1603011F82A2010F82B3B3A660A460A3601307606E150E0103161E606E4B7F0101 16706D6C03F07F6FD903E013F86E6C4948EBFFF8DA1FE0EB1F00DA0FFE13FE0203B512F8 DA007F13E0030790C7EBC0004D4C7ACA58>I121 D E %EndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 %%EndSetup %%Page: 1 1 1 0 bop Black Black Black Black 21 636 a Ft(Sp)t(ectral)53 b(Prop)t(erties)h(of)e(Finite)h(Quan)l(tum)e(Hall)j(Systems)3640 573 y Fs(\003)892 976 y Fr(Christian)36 b(F)-10 b(errari)37 b(and)i(Nicolas)e(Macris)1030 1268 y(Institut)h(de)h(Ph)m(ysique)f(Th)m (\023)-55 b(eorique)1078 1462 y(Ecole)38 b(P)m(olytec)m(hnique)e(F)m (\023)-55 b(ed)m(\023)g(erale)972 1619 y(CH)38 b(-)h(1015)f(Lausanne,)g (Switzerland)p Black Black 1630 2068 a Fq(Abstract)p Black Black 264 2240 a Fp(In)20 b(this)f(note)i(w)m(e)g(review)f(sp)s (ectral)f(prop)s(erties)g(of)i(magnetic)g(random)e(Sc)m(hr\177)-45 b(odinger)19 b(op)s(erators)128 2387 y Fo(H)204 2401 y Fn(!)281 2387 y Fp(=)27 b Fo(H)455 2401 y Fm(0)515 2387 y Fp(+)21 b Fo(V)660 2401 y Fn(!)731 2387 y Fp(+)g Fo(U)885 2402 y Fn(`)939 2387 y Fp(+)f Fo(U)1092 2401 y Fn(r)1162 2387 y Fp(de\014ned)30 b(on)i Fo(L)1666 2354 y Fm(2)1705 2387 y Fp(\()p Fl(R)e Fk(\002)1919 2313 y Fj(\002)1957 2387 y Fk(\000)2038 2351 y Fn(L)p 2038 2366 48 4 v 2044 2418 a Fm(2)2095 2387 y Fo(;)2146 2351 y Fn(L)p 2146 2366 V 2152 2418 a Fm(2)2204 2313 y Fj(\003)2257 2387 y Fo(;)g Fp(d)p Fo(x)15 b Fp(d)o Fo(y)s Fp(\))32 b(with)e(p)s(erio)s(dic)f(b)s(oundary)128 2534 y(conditions)35 b(along)j Fo(y)s Fp(.)61 b Fo(U)1015 2549 y Fn(`)1085 2534 y Fp(and)37 b Fo(U)1331 2548 y Fn(r)1406 2534 y Fp(are)h(t)m(w)m(o)h(con\014ning)d(p)s(oten)m(tials)g(for)h Fo(x)g Fk(\024)g(\000)2990 2498 y Fn(L)p 2990 2513 V 2996 2565 a Fm(2)3084 2534 y Fp(and)g Fo(x)g Fk(\025)3474 2498 y Fn(L)p 3474 2513 V 3480 2565 a Fm(2)128 2680 y Fp(resp)s(ectiv)m(ely)g(and)g(v)-5 b(anish)36 b(for)i Fk(\000)1331 2645 y Fn(L)p 1331 2660 V 1337 2712 a Fm(2)1426 2680 y Fk(\024)f Fo(x)h Fk(\024)1742 2645 y Fn(L)p 1742 2660 V 1748 2712 a Fm(2)1800 2680 y Fp(.)63 b(W)-8 b(e)39 b(describ)s(e)d(the)i(sp)s(ectrum)e(in)h(t)m(w)m(o)i(energy)128 2827 y(in)m(terv)-5 b(als)25 b(and)g(w)m(e)h(classify)f(it)g(according) h(to)h(the)f(quan)m(tum)g(mec)m(hanical)f(curren)m(t)h(of)g (eigenstates)128 2974 y(along)39 b(the)h(p)s(erio)s(dic)d(direction.)66 b(The)39 b(\014rst)g(in)m(terv)-5 b(al)39 b(lies)f(in)g(the)i(\014rst)e (Landau)h(band)f(of)i(the)128 3121 y(bulk)e(Hamiltonian,)j(and)f(con)m (tains)g(in)m(termixed)f(eigen)m(v)-5 b(alues)40 b(with)e(a)j(quan)m (tum)e(mec)m(hanical)128 3268 y(curren)m(t)31 b(of)g Fk(O)s Fp(\(1\))h(and)e Fk(O)1038 3167 y Fj(\020)1093 3268 y Fo(e)1135 3235 y Fi(\000)p Fn(\015)t(B)s Fm(\(log)14 b Fn(L)p Fm(\))1492 3211 y Fh(2)1531 3167 y Fj(\021)1617 3268 y Fp(resp)s(ectiv)m(ely)-8 b(.)42 b(The)31 b(second)g(in)m(terv)-5 b(al)30 b(lies)g(in)g(the)h(\014rst)128 3414 y(sp)s(ectral)i(gap)g(of)h (the)g(bulk)e(Hamiltonian,)h(and)g(con)m(tains)g(only)g(eigen)m(v)-5 b(alues)34 b(with)e(a)i(quan)m(tum)128 3561 y(mec)m(hanical)c(curren)m (t)g(of)h Fk(O)s Fp(\(1\).)128 3932 y Fg(1)161 b(In)l(tro)t(duction)128 4169 y Fp(In)21 b(this)g(note)i(w)m(e)f(review)f(recen)m(t)i(results)e (on)h(the)g(sp)s(ectrum)f(of)h(a)h(magnetic)f(random)g(Sc)m(hr\177)-45 b(odinger)128 4316 y(op)s(erator)37 b Fo(H)577 4330 y Fn(!)664 4316 y Fp(whic)m(h)f(describ)s(es)f(the)i(dynamics)f(of)h(an)g (electron)h(lying)d(on)i(a)h(cylinder)d(of)i(cir-)128 4462 y(cumference)31 b Fo(L)g Fp(and)f(whic)m(h)g(is)g(con\014ned)g (along)i(the)f(cylinder)e(axis)h(b)m(y)h(t)m(w)m(o)i(smo)s(oth)e (increasing)128 4609 y(p)s(oten)m(tials)39 b(whose)i(supp)s(orts)d(are) j(separated)g(b)m(y)f(a)h(distance)f Fo(L)p Fp(.)71 b(W)-8 b(e)41 b(supp)s(ose)e(our)h(particle)128 4756 y(spinless,)29 b(th)m(us)i(the)g(Zeeman)g(term)h(in)e(the)h(Hamiltonian)f(is)g (neglected.)44 b(The)30 b(complete)i(pro)s(ofs)128 4903 y(of)e(the)h(theorems)f(stated)i(here)e(can)h(b)s(e)e(found)g(in)g ([FM1)r(])h(and)g([FM2)q(].)264 5049 y(First)35 b(let)h(us)f(shortly)g (recall)h(previous)e(results)h(on)h(random)f(Sc)m(hr\177)-45 b(odinger)34 b(op)s(erators)j(with)128 5196 y(magnetic)32 b(\014eld)e(in)g(the)i(in\014nite)d(t)m(w)m(o)k(dimensional)c(plane)i Fl(R)2268 5163 y Fm(2)2314 5196 y Fp(.)44 b(W)-8 b(e)33 b(denote)f(b)m(y)g Fo(H)3039 5210 y Fm(0)3109 5196 y Fp(the)g(kinetic)128 5343 y(term)27 b Fo(H)418 5357 y Fm(0)482 5343 y Fp(=)e(\()p Fo(p)14 b Fk(\000)g Fo(A)p Fp(\))861 5310 y Fm(2)900 5343 y Fp(,)28 b(where)f Fo(A)g Fp(is)g(the)g(v)m(ector)i(p)s(oten)m(tial)d(asso)s(ciated)i(to)g(a)f (constan)m(t)i(magnetic)128 5490 y(\014eld)h Fo(B)5 b Fp(.)46 b(The)32 b(sp)s(ectrum)f(of)h Fo(H)1240 5504 y Fm(0)1311 5490 y Fp(is)f(giv)m(en)h(b)m(y)h(the)f(Landau)f(lev)m(els) h Fk(f)p Fp(\(2)p Fo(n)21 b Fp(+)f(1\))p Fo(B)30 b Fp(:)c Fo(n)f Fk(2)g Fl(N)6 b Fk(g)h Fp(.)46 b(The)128 5637 y(bulk)28 b(Hamiltonian)h(is)1542 5783 y Fo(H)1625 5746 y Fn(b)1618 5806 y(!)1693 5783 y Fp(=)c Fo(H)1865 5797 y Fm(0)1924 5783 y Fp(+)20 b Fo(V)2068 5797 y Fn(!)3345 5783 y Fp(\(1.1\))p Black -116 5844 1557 4 v -5 5905 a Ff(\003)33 5935 y Fe(Accepted)28 b(for)f(J.)h(Op)r(er.)36 b(Theor.)p Black Black 1806 6184 a Fd(1)p Black eop %%Page: 2 2 2 1 bop Black Black 128 171 a Fp(where)82 b Fo(V)496 185 y Fn(!)630 171 y Fp(is)g(a)h(Anderson-lik)m(e)f(random)g(p)s(oten)m (tial.)199 b(The)82 b(sp)s(ectrum)g(of)90 b(\(1.1\))128 317 y(is)101 b(con)m(tained)h(in)e(Landau)h(bands)g(around)g(eac)m(h)i (Landau)e(lev)m(el,)119 b Fo(\033)s Fp(\()p Fo(H)3238 284 y Fn(b)3231 340 y(!)3282 317 y Fp(\))145 b Fk(\032)128 396 y Fj(S)203 491 y Fn(n)p Fi(\025)p Fm(0)356 464 y Fp([\(2)p Fo(n)21 b Fp(+)e(1\))p Fo(B)26 b Fk(\000)20 b Fo(V)946 478 y Fm(0)985 464 y Fo(;)15 b Fp(\(2)p Fo(n)21 b Fp(+)f(1\))p Fo(B)26 b Fp(+)20 b Fo(V)1591 478 y Fm(0)1630 464 y Fp(])57 b(where)f Fo(V)2054 478 y Fm(0)2163 464 y Fp(=)69 b Fk(k)p Fo(V)2401 478 y Fn(!)2452 464 y Fk(k)p Fp(,)64 b(and)56 b(if)f Fo(V)2951 478 y Fm(0)3060 464 y Fo(<)69 b(B)61 b Fp(there)128 611 y(are)35 b(op)s(en)f(sp)s(ectral)g (gaps)g Fo(G)1137 625 y Fn(n)1216 611 y Fk(\023)e Fp(\()q(\(2)p Fo(n)20 b Fp(+)g(1\))p Fo(B)26 b Fp(+)20 b Fo(V)1920 625 y Fm(0)1959 611 y Fo(;)15 b Fp(\(2)p Fo(n)21 b Fp(+)f(3\))p Fo(B)25 b Fk(\000)20 b Fo(V)2564 625 y Fm(0)2604 611 y Fp(\))35 b(\()p Fo(n)d Fk(2)g Fl(N)7 b Fp(\).)60 b(It)34 b(is)g(pro)m(v)m(en)128 758 y(that)52 b(near)f(the)g(band)f(edges)i (the)g(sp)s(ectrum)e(of)h Fo(H)2061 725 y Fn(b)2054 780 y(!)2156 758 y Fp(is)f(almost)h(surely)f(pure)g(p)s(oin)m(t)h(with)128 905 y(exp)s(onen)m(tially)29 b(lo)s(calized)h(eigenfunctions)g([DMP1)q (],)i([DMP2)q(],)g([CH],)f([BCH)q(],)h([W].)43 b(There)31 b(are)128 1051 y(no)h(rigorous)g(results)f(for)h(energies)h(at)g(the)g (band)e(cen)m(ters,)j(except)g(for)e(a)h(sp)s(ecial)e(mo)s(del)h(where) 128 1198 y(the)e(impurities)d(are)k(p)s(oin)m(t)e(scatterers)j([DMP3)q (],)f([DMP4)r(].)264 1345 y(W)-8 b(e)26 b(no)m(w)f(add)f(a)h(w)m(all)f (p)s(oten)m(tial,)i(translation)e(in)m(v)-5 b(arian)m(t)24 b(along)h(the)g Fo(y)s Fk(\000)p Fp(direction,)f(suc)m(h)h(that)128 1492 y Fo(U)190 1507 y Fn(`)223 1492 y Fp(\()p Fo(x)p Fp(\))37 b(is)f(con\014ning)g(for)h Fo(x)f Fk(\024)g(\000)1298 1456 y Fn(L)p 1298 1471 48 4 v 1304 1523 a Fm(2)1393 1492 y Fp(and)g Fo(U)1638 1507 y Fn(`)1671 1492 y Fp(\()p Fo(x)p Fp(\))h(=)f(0)i(for)e Fo(x)h Fk(\025)f(\000)2442 1456 y Fn(L)p 2442 1471 V 2448 1523 a Fm(2)2499 1492 y Fp(.)61 b(W)-8 b(e)38 b(ha)m(v)m(e)h(a)e(semi-in\014nite)128 1638 y(system)30 b(with)f(a)i(Hamiltonian)1404 1785 y Fo(H)1487 1748 y Fn(si)1480 1808 y(!)1573 1785 y Fp(=)25 b Fo(H)1745 1799 y Fm(0)1805 1785 y Fp(+)19 b Fo(V)1948 1799 y Fn(!)2019 1785 y Fp(+)h Fo(U)2172 1800 y Fn(`)2230 1785 y Fo(:)1090 b Fp(\(1.2\))128 1986 y(The)43 b(sp)s(ectrum)f(con)m (tains)i(the)g(in)m(terv)-5 b(al)42 b([)p Fo(B)5 b(;)15 b Fp(+)p Fk(1)p Fp(\).)81 b(F)-8 b(or)44 b(this)f(system)g(one)h(can)g (sho)m(w)f(that,)128 2133 y(for)32 b(energies)g(in)f(in)m(terv)-5 b(als)32 b(inside)e(the)j(gaps)f(of)h(the)g(bulk)d(Hamiltonian,)i(the)h (a)m(v)m(erage)i(v)m(elo)s(cit)m(y)128 2280 y(\()p Fo( )s(;)15 b(v)309 2294 y Fn(y)351 2280 y Fo( )s Fp(\))41 b(in)d(the)i Fo(y)i Fp(direction,)f(of)f(an)f(assumed)g(eigenstate)i Fo( )i Fp(do)s(es)c(not)h(v)-5 b(anish.)67 b(Since)38 b(the)128 2426 y(v)m(elo)s(cit)m(y)32 b Fo(v)509 2440 y Fn(y)582 2426 y Fp(is)e(the)i(comm)m(utator)h(b)s(et)m(w)m(een)f Fk(\000)p Fo(iy)i Fp(and)d(the)h(Hamiltonian,)e(the)i(Virial)e(Theorem) 128 2573 y(implies)40 b(that)k(an)f(eigenstate)i(cannot)f(exist,)j(and) 42 b(that)i(therefore)g(the)g(sp)s(ectrum)e(is)g(purely)128 2720 y(con)m(tin)m(uous)25 b(inside)f(the)i(gaps)f(of)h(the)g(bulk)e (Hamiltonian)g([MMP)q(],)j([F)q(].)39 b(By)26 b(Mourre)g(theory)g(one) 128 2867 y(can)k(sho)m(w)h(that)g(the)f(sp)s(ectrum)f(therein)h(is)f (purely)g(absolutely)g(con)m(tin)m(uous)h([F)m(GW)r(],)h([dBP].)264 3013 y(Finally)f(w)m(e)i(can)g(add)f(a)i(second)f(w)m(all)e(p)s(oten)m (tial)i Fo(U)2067 3027 y Fn(r)2137 3013 y Fp(suc)m(h)f(that)i Fo(U)2604 3027 y Fn(r)2642 3013 y Fp(\()p Fo(x)p Fp(\))28 b(=)f(0)33 b(for)e Fo(x)d Fk(\024)3296 2978 y Fn(L)p 3296 2993 V 3302 3045 a Fm(2)3386 3013 y Fp(and)128 3160 y(whic)m(h)i(is)g(con\014ning)g(for)h Fo(x)26 b Fk(\025)1196 3124 y Fn(L)p 1196 3139 V 1202 3192 a Fm(2)1254 3160 y Fp(.)44 b(So)31 b(the)g(particle)f(is)h(con\014ned)f(b)s(et)m(w)m (een)i Fo(x)27 b Fp(=)f Fk(\000)2997 3124 y Fn(L)p 2997 3139 V 3003 3192 a Fm(2)3086 3160 y Fp(and)k Fo(x)d Fp(=)3449 3124 y Fn(L)p 3449 3139 V 3455 3192 a Fm(2)3507 3160 y Fp(.)128 3307 y(The)j(Hamiltonian)e(has)i(the)h(form)1308 3545 y Fo(H)1384 3559 y Fn(!)1459 3545 y Fp(=)25 b Fo(H)1631 3559 y Fm(0)1690 3545 y Fp(+)20 b Fo(V)1834 3559 y Fn(!)1905 3545 y Fp(+)g Fo(U)2058 3560 y Fn(`)2111 3545 y Fp(+)g Fo(U)2264 3559 y Fn(r)2327 3545 y Fo(:)993 b Fp(\(1.3\))p Black Black Black 456 5129 a @beginspecial 0 @llx 0 @lly 331 @urx 163 @ury 3310 @rwi @setspecial %%BeginDocument: model.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: model.pstex %%Creator: fig2dev Version 3.2 Patchlevel 3c %%CreationDate: Wed Feb 6 08:54:35 2002 %%For: ferrari@iptdec1.epfl.ch (Christian Ferrari) %%BoundingBox: 0 0 331 163 %%Magnification: 0.6000 %%EndComments /MyAppDict 100 dict dup begin def /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 163 moveto 0 0 lineto 331 0 lineto 331 163 lineto closepath clip newpath -16.0 238.0 translate 1 -1 scale % This junk string is used by the show operators /PATsstr 1 string def /PATawidthshow { % cx cy cchar rx ry string % Loop over each character in the string { % cx cy cchar rx ry char % Show the character dup % cx cy cchar rx ry char char PATsstr dup 0 4 -1 roll put % cx cy cchar rx ry char (char) false charpath % cx cy cchar rx ry char /clip load PATdraw % Move past the character (charpath modified the % current point) currentpoint % cx cy cchar rx ry char x y newpath moveto % cx cy cchar rx ry char % Reposition by cx,cy if the character in the string is cchar 3 index eq { % cx cy cchar rx ry 4 index 4 index rmoveto } if % Reposition all characters by rx ry 2 copy rmoveto % cx cy cchar rx ry } forall pop pop pop pop pop % - currentpoint newpath moveto } bind def /PATcg { 7 dict dup begin /lw currentlinewidth def /lc currentlinecap def /lj currentlinejoin def /ml currentmiterlimit def /ds [ currentdash ] def /cc [ currentrgbcolor ] def /cm matrix currentmatrix def end } bind def % PATdraw - calculates the boundaries of the object and % fills it with the current pattern /PATdraw { % proc save exch PATpcalc % proc nw nh px py 5 -1 roll exec % nw nh px py newpath PATfill % - restore } bind def % PATfill - performs the tiling for the shape /PATfill { % nw nh px py PATfill - PATDict /CurrentPattern get dup begin setfont % Set the coordinate system to Pattern Space PatternGState PATsg % Set the color for uncolored pattezns PaintType 2 eq { PATDict /PColor get PATsc } if % Create the string for showing 3 index string % nw nh px py str % Loop for each of the pattern sources 0 1 Multi 1 sub { % nw nh px py str source % Move to the starting location 3 index 3 index % nw nh px py str source px py moveto % nw nh px py str source % For multiple sources, set the appropriate color Multi 1 ne { dup PC exch get PATsc } if % Set the appropriate string for the source 0 1 7 index 1 sub { 2 index exch 2 index put } for pop % Loop over the number of vertical cells 3 index % nw nh px py str nh { % nw nh px py str currentpoint % nw nh px py str cx cy 2 index oldshow % nw nh px py str cx cy YStep add moveto % nw nh px py str } repeat % nw nh px py str } for 5 { pop } repeat end } bind def % PATkshow - kshow with the current pattezn /PATkshow { % proc string exch bind % string proc 1 index 0 get % string proc char % Loop over all but the last character in the string 0 1 4 index length 2 sub { % string proc char idx % Find the n+1th character in the string 3 index exch 1 add get % string proe char char+1 exch 2 copy % strinq proc char+1 char char+1 char % Now show the nth character PATsstr dup 0 4 -1 roll put % string proc chr+1 chr chr+1 (chr) false charpath % string proc char+1 char char+1 /clip load PATdraw % Move past the character (charpath modified the current point) currentpoint newpath moveto % Execute the user proc (should consume char and char+1) mark 3 1 roll % string proc char+1 mark char char+1 4 index exec % string proc char+1 mark... cleartomark % string proc char+1 } for % Now display the last character PATsstr dup 0 4 -1 roll put % string proc (char+1) false charpath % string proc /clip load PATdraw neewath pop pop % - } bind def % PATmp - the makepattern equivalent /PATmp { % patdict patmtx PATmp patinstance exch dup length 7 add % We will add 6 new entries plus 1 FID dict copy % Create a new dictionary begin % Matrix to install when painting the pattern TilingType PATtcalc /PatternGState PATcg def PatternGState /cm 3 -1 roll put % Check for multi pattern sources (Level 1 fast color patterns) currentdict /Multi known not { /Multi 1 def } if % Font dictionary definitions /FontType 3 def % Create a dummy encoding vector /Encoding 256 array def 3 string 0 1 255 { Encoding exch dup 3 index cvs cvn put } for pop /FontMatrix matrix def /FontBBox BBox def /BuildChar { mark 3 1 roll % mark dict char exch begin Multi 1 ne {PaintData exch get}{pop} ifelse % mark [paintdata] PaintType 2 eq Multi 1 ne or { XStep 0 FontBBox aload pop setcachedevice } { XStep 0 setcharwidth } ifelse currentdict % mark [paintdata] dict /PaintProc load % mark [paintdata] dict paintproc end gsave false PATredef exec true PATredef grestore cleartomark % - } bind def currentdict end % newdict /foo exch % /foo newlict definefont % newfont } bind def % PATpcalc - calculates the starting point and width/height % of the tile fill for the shape /PATpcalc { % - PATpcalc nw nh px py PATDict /CurrentPattern get begin gsave % Set up the coordinate system to Pattern Space % and lock down pattern PatternGState /cm get setmatrix BBox aload pop pop pop translate % Determine the bounding box of the shape pathbbox % llx lly urx ury grestore % Determine (nw, nh) the # of cells to paint width and height PatHeight div ceiling % llx lly urx qh 4 1 roll % qh llx lly urx PatWidth div ceiling % qh llx lly qw 4 1 roll % qw qh llx lly PatHeight div floor % qw qh llx ph 4 1 roll % ph qw qh llx PatWidth div floor % ph qw qh pw 4 1 roll % pw ph qw qh 2 index sub cvi abs % pw ph qs qh-ph exch 3 index sub cvi abs exch % pw ph nw=qw-pw nh=qh-ph % Determine the starting point of the pattern fill %(px, py) 4 2 roll % nw nh pw ph PatHeight mul % nw nh pw py exch % nw nh py pw PatWidth mul exch % nw nh px py end } bind def % Save the original routines so that we can use them later on /oldfill /fill load def /oldeofill /eofill load def /oldstroke /stroke load def /oldshow /show load def /oldashow /ashow load def /oldwidthshow /widthshow load def /oldawidthshow /awidthshow load def /oldkshow /kshow load def % These defs are necessary so that subsequent procs don't bind in % the originals /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def /PATredef { MyAppDict begin { /fill { /clip load PATdraw newpath } bind def /eofill { /eoclip load PATdraw newpath } bind def /stroke { PATstroke } bind def /show { 0 0 null 0 0 6 -1 roll PATawidthshow } bind def /ashow { 0 0 null 6 3 roll PATawidthshow } bind def /widthshow { 0 0 3 -1 roll PATawidthshow } bind def /awidthshow { PATawidthshow } bind def /kshow { PATkshow } bind def } { /fill { oldfill } bind def /eofill { oldeofill } bind def /stroke { oldstroke } bind def /show { oldshow } bind def /ashow { oldashow } bind def /widthshow { oldwidthshow } bind def /awidthshow { oldawidthshow } bind def /kshow { oldkshow } bind def } ifelse end } bind def false PATredef % Conditionally define setcmykcolor if not available /setcmykcolor where { pop } { /setcmykcolor { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat setrgbcolor - pop } bind def } ifelse /PATsc { % colorarray aload length % c1 ... cn length dup 1 eq { pop setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /PATsg { % dict begin lw setlinewidth lc setlinecap lj setlinejoin ml setmiterlimit ds aload pop setdash cc aload pop setrgbcolor cm setmatrix end } bind def /PATDict 3 dict def /PATsp { true PATredef PATDict begin /CurrentPattern exch def % If it's an uncolored pattern, save the color CurrentPattern /PaintType get 2 eq { /PColor exch def } if /CColor [ currentrgbcolor ] def end } bind def % PATstroke - stroke with the current pattern /PATstroke { countdictstack save mark { currentpoint strokepath moveto PATpcalc % proc nw nh px py clip newpath PATfill } stopped { (*** PATstroke Warning: Path is too complex, stroking with gray) = cleartomark restore countdictstack exch sub dup 0 gt { { end } repeat } { pop } ifelse gsave 0.5 setgray oldstroke grestore } { pop restore pop } ifelse newpath } bind def /PATtcalc { % modmtx tilingtype PATtcalc tilematrix % Note: tiling types 2 and 3 are not supported gsave exch concat % tilingtype matrix currentmatrix exch % cmtx tilingtype % Tiling type 1 and 3: constant spacing 2 ne { % Distort the pattern so that it occupies % an integral number of device pixels dup 4 get exch dup 5 get exch % tx ty cmtx XStep 0 dtransform round exch round exch % tx ty cmtx dx.x dx.y XStep div exch XStep div exch % tx ty cmtx a b 0 YStep dtransform round exch round exch % tx ty cmtx a b dy.x dy.y YStep div exch YStep div exch % tx ty cmtx a b c d 7 -3 roll astore % { a b c d tx ty } } if grestore } bind def /PATusp { false PATredef PATDict begin CColor PATsc end } bind def % left45 11 dict begin /PaintType 1 def /PatternType 1 def /TilingType 1 def /BBox [0 0 1 1] def /XStep 1 def /YStep 1 def /PatWidth 1 def /PatHeight 1 def /Multi 2 def /PaintData [ { clippath } bind { 32 32 true [ 32 0 0 -32 0 32 ] {<808080804040404020202020101010100808080804040404 020202020101010180808080404040402020202010101010 080808080404040402020202010101018080808040404040 202020201010101008080808040404040202020201010101 808080804040404020202020101010100808080804040404 0202020201010101>} imagemask } bind ] def /PaintProc { pop exec fill } def currentdict end /P4 exch def /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /reencdict 12 dict def /ReEncode { reencdict begin /newcodesandnames exch def /newfontname exch def /basefontname exch def /basefontdict basefontname findfont def /newfont basefontdict maxlength dict def basefontdict { exch dup /FID ne { dup /Encoding eq { exch dup length array copy newfont 3 1 roll put } { exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall newfont /FontName newfontname put newcodesandnames aload pop 128 1 255 { newfont /Encoding get exch /.notdef put } for newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat newfontname newfont definefont pop end } def /isovec [ 8#055 /minus 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde 8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis 8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron 8#220 /dotlessi 8#230 /oe 8#231 /OE 8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling 8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis 8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot 8#255 /hyphen 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus 8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph 8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine 8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf 8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute 8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring 8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute 8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute 8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve 8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply 8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex 8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave 8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring 8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute 8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute 8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve 8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide 8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex 8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def /Times-Roman /Times-Roman-iso isovec ReEncode /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.03600 0.03600 sc % % Fig objects follow % % Polyline 7.500 slw [45] 0 sd n 2175 6300 m 2400 5850 l 2550 6150 l 2850 5775 l 3000 6225 l 3225 5475 l 3450 6300 l 3525 6000 l 3675 5850 l 3900 5775 l 3975 5625 l 4125 6075 l 4425 6300 l 4500 6150 l 4650 6000 l 5025 6300 l 5250 5850 l 5550 6225 l 5550 5850 l 5775 6225 l 6000 5925 l 6375 6075 l 6525 5775 l 6825 6300 l 6900 5850 l 7050 6225 l 7125 5850 l 7425 6075 l gs col0 s gr [] 0 sd % Polyline n 1185 6000 m 465 6000 l gs /PC [[1.00 1.00 1.00] [0.00 0.00 0.00]] def 15.00 15.00 sc P4 [16 0 0 -16 31.00 400.00] PATmp PATsp ef gr PATusp gs col0 s gr % Polyline gs clippath 9615 6030 m 9615 5970 l 9430 5970 l 9580 6000 l 9430 6030 l cp eoclip n 1200 6000 m 9600 6000 l gs col7 0.20 shd ef gr gs col0 s gr gr % arrowhead n 9430 6030 m 9580 6000 l 9430 5970 l 9460 6000 l 9430 6030 l cp gs 0.00 setgray ef gr col0 s % Polyline n 7425 5925 m 7425 6150 l gs col0 s gr % Polyline n 2175 5925 m 2175 6150 l gs col0 s gr % Polyline 2 slj n 2175 6000 m 2174 6000 l 2171 5999 l 2162 5997 l 2147 5993 l 2127 5988 l 2102 5981 l 2075 5974 l 2049 5967 l 2023 5961 l 1999 5954 l 1978 5948 l 1959 5943 l 1942 5938 l 1927 5934 l 1913 5929 l 1900 5925 l 1886 5920 l 1871 5915 l 1857 5910 l 1843 5904 l 1830 5898 l 1816 5891 l 1802 5884 l 1788 5877 l 1775 5869 l 1762 5861 l 1749 5852 l 1737 5844 l 1725 5835 l 1713 5825 l 1702 5816 l 1690 5807 l 1678 5796 l 1666 5785 l 1653 5773 l 1640 5760 l 1626 5747 l 1613 5732 l 1599 5718 l 1585 5703 l 1572 5688 l 1559 5672 l 1547 5657 l 1535 5642 l 1523 5627 l 1513 5613 l 1504 5600 l 1495 5588 l 1487 5575 l 1478 5561 l 1470 5546 l 1461 5531 l 1452 5515 l 1442 5497 l 1433 5479 l 1423 5459 l 1414 5439 l 1404 5418 l 1394 5396 l 1384 5374 l 1375 5351 l 1365 5327 l 1355 5303 l 1345 5278 l 1335 5252 l 1325 5225 l 1318 5206 l 1311 5187 l 1304 5167 l 1296 5146 l 1288 5124 l 1280 5101 l 1272 5077 l 1263 5052 l 1254 5026 l 1245 4999 l 1236 4971 l 1226 4942 l 1216 4913 l 1207 4882 l 1197 4851 l 1186 4819 l 1176 4786 l 1166 4754 l 1156 4721 l 1146 4687 l 1136 4654 l 1126 4620 l 1116 4586 l 1106 4553 l 1097 4519 l 1087 4485 l 1078 4452 l 1068 4418 l 1059 4384 l 1050 4350 l 1042 4319 l 1034 4289 l 1026 4257 l 1017 4225 l 1009 4192 l 1001 4159 l 992 4124 l 984 4090 l 975 4054 l 966 4018 l 958 3981 l 949 3944 l 940 3906 l 931 3868 l 923 3829 l 914 3790 l 905 3752 l 897 3713 l 888 3674 l 880 3636 l 872 3598 l 864 3561 l 856 3524 l 849 3487 l 842 3452 l 835 3417 l 828 3382 l 822 3349 l 815 3316 l 809 3284 l 804 3253 l 798 3222 l 793 3192 l 788 3163 l 782 3130 l 776 3097 l 771 3065 l 766 3032 l 761 3000 l 757 2967 l 752 2934 l 747 2899 l 743 2864 l 738 2827 l 733 2790 l 729 2750 l 724 2710 l 719 2668 l 714 2625 l 709 2581 l 705 2537 l 700 2494 l 696 2453 l 692 2414 l 688 2377 l 685 2345 l 682 2317 l 679 2295 l 678 2277 l 676 2264 l 676 2256 l 675 2252 l 675 2250 l gs col0 s gr % Polyline 0 slj gs clippath 4830 2085 m 4770 2085 l 4770 2270 l 4800 2120 l 4830 2270 l cp eoclip n 4800 2100 m 4800 6525 l gs col0 s gr gr % arrowhead n 4830 2270 m 4800 2120 l 4770 2270 l 4800 2240 l 4830 2270 l cp gs 0.00 setgray ef gr col0 s % Polyline 2 slj n 7425 6000 m 7426 6000 l 7429 5999 l 7438 5997 l 7453 5993 l 7473 5988 l 7498 5981 l 7525 5974 l 7551 5967 l 7577 5961 l 7601 5954 l 7622 5948 l 7641 5943 l 7658 5938 l 7673 5934 l 7687 5929 l 7700 5925 l 7714 5920 l 7729 5915 l 7743 5910 l 7757 5904 l 7770 5898 l 7784 5891 l 7798 5884 l 7812 5877 l 7825 5869 l 7838 5861 l 7851 5852 l 7863 5844 l 7875 5835 l 7888 5825 l 7898 5816 l 7910 5807 l 7922 5796 l 7934 5785 l 7947 5773 l 7960 5760 l 7974 5747 l 7988 5732 l 8001 5718 l 8015 5703 l 8028 5688 l 8041 5672 l 8053 5657 l 8065 5642 l 8077 5627 l 8088 5613 l 8096 5600 l 8105 5588 l 8113 5575 l 8122 5561 l 8130 5546 l 8139 5531 l 8148 5515 l 8158 5497 l 8167 5479 l 8177 5459 l 8186 5439 l 8196 5418 l 8206 5396 l 8216 5374 l 8225 5351 l 8235 5327 l 8245 5303 l 8255 5278 l 8265 5252 l 8275 5225 l 8282 5206 l 8289 5187 l 8296 5167 l 8304 5146 l 8312 5124 l 8320 5101 l 8328 5077 l 8337 5052 l 8346 5026 l 8355 4999 l 8364 4971 l 8374 4942 l 8384 4913 l 8393 4882 l 8403 4851 l 8414 4819 l 8424 4786 l 8434 4754 l 8444 4721 l 8454 4687 l 8464 4654 l 8474 4620 l 8484 4586 l 8494 4553 l 8503 4519 l 8513 4485 l 8522 4452 l 8532 4418 l 8541 4384 l 8550 4350 l 8558 4319 l 8566 4289 l 8574 4257 l 8583 4225 l 8591 4192 l 8599 4159 l 8608 4124 l 8616 4090 l 8625 4054 l 8634 4018 l 8642 3981 l 8651 3944 l 8660 3906 l 8669 3868 l 8677 3829 l 8686 3790 l 8695 3752 l 8703 3713 l 8712 3674 l 8720 3636 l 8728 3598 l 8736 3561 l 8744 3524 l 8751 3487 l 8758 3452 l 8765 3417 l 8772 3382 l 8778 3349 l 8785 3316 l 8791 3284 l 8796 3253 l 8802 3222 l 8807 3192 l 8813 3163 l 8818 3130 l 8824 3097 l 8829 3065 l 8834 3032 l 8839 3000 l 8843 2967 l 8848 2934 l 8853 2899 l 8857 2864 l 8862 2827 l 8867 2790 l 8871 2750 l 8876 2710 l 8881 2668 l 8886 2625 l 8891 2581 l 8895 2537 l 8900 2494 l 8904 2453 l 8908 2414 l 8912 2377 l 8915 2345 l 8918 2317 l 8921 2295 l 8922 2277 l 8924 2264 l 8924 2256 l 8925 2252 l 8925 2250 l gs col0 s gr $F2psEnd rs end %%EndDocument @endspecial 0 0 0 TeXcolorrgb 1828 4859 a Fo(V)1881 4873 y Fn(!)p Black 0 0 0 TeXcolorrgb 3133 5039 a Fo(x)p Black 0 0 0 TeXcolorrgb 590 3914 a(U)652 3929 y Fn(`)p Black 0 0 0 TeXcolorrgb 2818 3914 a Fo(U)2880 3928 y Fn(r)p Black 0 0 0 TeXcolorrgb 860 5129 a Fk(\000)941 5093 y Fn(L)p 941 5108 V 947 5160 a Fm(2)p Black 0 0 0 TeXcolorrgb 2535 5093 a Fn(L)p 2535 5108 V 2541 5160 a Fm(2)p Black Black 983 5468 a Fd(Figure)31 b(1:)44 b Fc(The)33 b(p)-5 b(otentials)34 b(along)g(the)f Fo(x)p Fc(-axes.)p Black Black 264 5728 a Fp(Additionally)28 b(w)m(e)j(mak)m(e)h(the)f Fo(y)s Fk(\000)p Fp(direction)e(p)s(erio)s (dic)f(of)j(length)f Fo(L)g Fp(\()p Fo(L)h Fp(a)g(large)g(parameter\),) 128 5874 y(this)e(corresp)s(ond)g(to)i(a)g(\014nite,)f(macroscopic)g (cylindrical)e(geometry)-8 b(.)p Black 1806 6184 a Fd(2)p Black eop %%Page: 3 3 3 2 bop Black Black 264 171 a Fp(Other)26 b(mo)s(dels)g(with)f (con\014nemen)m(t)i(in)e(the)i Fo(x)p Fk(\000)p Fp(direction)e(but)h (without)g(p.b.c.)39 b(along)27 b Fo(y)i Fp(ha)m(v)m(e)128 317 y(b)s(een)34 b(studied.)53 b(The)34 b(\014rst)g(consists)h(of)g(a)g (parab)s(olic)e(c)m(hannel)i(where)f Fo(U)2692 332 y Fn(`)2748 317 y Fp(+)23 b Fo(U)2904 331 y Fn(r)2977 317 y Fp(is)34 b(replaced)g(b)m(y)128 464 y(a)h(parab)s(olic)f (con\014nemen)m(t)i Fo(\015)5 b(x)1227 431 y Fm(2)1266 464 y Fp(,)37 b(in)d(this)h(case)h(it)f(is)f(sho)m(wn)h(that)h(if)f (the)g(p)s(erturbation)e(\()p Fo(V)3370 478 y Fn(!)3457 464 y Fp(in)128 611 y(our)i(case\))i(is)d(small)g(enough)h(in)f(a)i (suitable)e(sense)i(and)f(satis\014es)g(a)g(w)m(eak)i(deca)m(y)f (condition)f(in)128 758 y(the)e Fo(y)s Fk(\000)p Fp(direction,)g(there) g(exists)h(in)m(terv)-5 b(als)32 b(of)i(absolutely)e(con)m(tin)m(uous)h (sp)s(ectrum)f([EJK].)50 b(The)128 905 y(second)36 b(mo)s(del,)g(more)g (close)g(to)g(ours,)h(consists)e(to)i(tak)m(e)g(t)m(w)m(o)h(step)d(w)m (alls)g(of)h(\014nite)f(heigh)m(t)h(for)128 1051 y Fo(U)190 1066 y Fn(`)257 1051 y Fp(and)d Fo(U)499 1065 y Fn(r)537 1051 y Fp(.)51 b(In)34 b(this)e(case)k(an)d(initial)f(state)j(lo)s (calized)e(in)f(energy)j(in)d(the)i(sp)s(ectral)g(gap)g(of)g(the)128 1198 y(bulk)f(Hamiltonian)g(and)h(near)g(the)h(left)g(\(resp.)53 b(righ)m(t\))34 b(w)m(all)g(has)h(a)g(p)s(ositiv)m(e)e(\(resp.)54 b(negativ)m(e\))128 1345 y(v)m(elo)s(cit)m(y)31 b(up)e(to)i(a)g (\014nite)e(time,)h(limited)e(b)m(y)j(tunneling)d(e\013ect)k(b)s(et)m (w)m(een)f(the)f(t)m(w)m(o)i(w)m(alls)d([C].)264 1492 y(The)37 b(ph)m(ysical)f(in)m(terest)h(of)g(our)g(mo)s(del)f(is)g (related)h(to)h(the)g(in)m(tegral)f(quan)m(tum)f(Hall)h(e\013ect)128 1638 y([PG].)61 b(F)-8 b(or)38 b(the)g(explanation)e(of)h(this)g (e\013ect)h(Halp)s(erin)d([H])j(p)s(oin)m(ted)e(out)h(the)h(imp)s (ortance)e(of)128 1785 y(the)28 b(b)s(oundary)e(diamagnetic)i(curren)m (ts.)39 b(Since)27 b(man)m(y)h(features)h(of)f(the)g(in)m(tegral)g (quan)m(tum)f(Hall)128 1932 y(e\013ect)i(can)g(b)s(e)e(describ)s(ed)f (in)h(the)h(framew)m(ork)h(of)f(one)g(particle)g(random)f(magnetic)i (Sc)m(hr\177)-45 b(odinger)128 2079 y(op)s(erators)31 b(it)f(is)g(imp)s(ortan)m(t)g(to)i(understand)d(their)g(sp)s(ectral)i (prop)s(erties)e(for)h(\014nite)g(but)g(macro-)128 2226 y(scopic)g(samples)f(with)g(b)s(oundaries.)128 2596 y Fg(2)161 b(The)53 b(mo)t(del)128 2833 y Fp(The)30 b(family)e(of)j (random)e(Sc)m(hr\177)-45 b(odinger)29 b(op)s(erators)i(that)g(w)m(e)g (w)m(an)m(t)g(to)g(study)f(is)864 3044 y Fo(H)940 3058 y Fn(!)1015 3044 y Fp(=)25 b Fo(p)1157 3006 y Fm(2)1157 3067 y Fn(x)1221 3044 y Fp(+)20 b(\()p Fo(p)1393 3058 y Fn(y)1455 3044 y Fk(\000)f Fo(B)5 b(x)p Fp(\))1706 3002 y Fm(2)1766 3044 y Fp(+)20 b Fo(V)1910 3058 y Fn(!)1981 3044 y Fp(+)f Fo(U)2133 3058 y Fn(r)2192 3044 y Fp(+)h Fo(U)2345 3059 y Fn(`)2559 3044 y Fo(!)29 b Fk(2)24 b Fp(\012)549 b(\(2.1\))128 3255 y(these)42 b(are)g(densely)e(de\014ned)g (self-adjoin)m(t)h(op)s(erators)h(acting)g(in)e(the)i(Hilb)s(ert)e (space)i Fo(L)3294 3222 y Fm(2)3333 3255 y Fp(\()p Fl(R)37 b Fk(\002)128 3329 y Fj(\002)166 3402 y Fk(\000)247 3366 y Fn(L)p 247 3381 48 4 v 253 3434 a Fm(2)304 3402 y Fo(;)355 3366 y Fn(L)p 355 3381 V 361 3434 a Fm(2)412 3329 y Fj(\003)466 3402 y Fo(;)30 b Fp(d)p Fo(x)15 b Fp(d)o Fo(y)s Fp(\))41 b(with)e(p)s(erio)s(dic)f(b)s(oundary)g(conditions)h(along)i Fo(y)s Fp(:)60 b Fo( )2717 3329 y Fj(\000)2758 3402 y Fo(x;)15 b Fk(\000)2931 3366 y Fn(L)p 2931 3381 V 2937 3434 a Fm(2)2989 3329 y Fj(\001)3073 3402 y Fp(=)42 b Fo( )3263 3329 y Fj(\000)3305 3402 y Fo(x;)3407 3366 y Fn(L)p 3407 3381 V 3413 3434 a Fm(2)3465 3329 y Fj(\001)3507 3402 y Fp(,)128 3549 y Fo(x)26 b Fk(2)f Fl(R)s Fp(.)48 b Fo(H)501 3563 y Fm(0)566 3549 y Fp(=)26 b Fo(p)709 3516 y Fm(2)709 3572 y Fn(x)773 3549 y Fp(+)20 b(\()q Fo(p)946 3563 y Fn(y)1007 3549 y Fk(\000)g Fo(B)5 b(x)p Fp(\))1259 3507 y Fm(2)1329 3549 y Fp(is)30 b(the)h(kinetic)f (Hamiltonian)f(written)h(in)f(Landau)h(gauge,)j(its)128 3696 y(sp)s(ectrum)c(consists)h(in)f(in\014nitely)e(degenerate)32 b(eigen)m(v)-5 b(alues)1004 3907 y Fo(\033)s Fp(\()p Fo(H)1170 3921 y Fm(0)1209 3907 y Fp(\))26 b(=)f Fo(\033)1418 3921 y Fn(ess)1520 3907 y Fp(\()p Fo(H)1631 3921 y Fm(0)1670 3907 y Fp(\))h(=)f Fk(f)p Fp(\(2)p Fo(n)c Fp(+)f(1\))p Fo(B)5 b Fp(;)15 b Fo(n)26 b Fk(2)e Fl(N)7 b Fk(g)47 b Fo(:)689 b Fp(\(2.2\))128 4119 y(The)22 b(t)m(w)m(o)j(con\014ning)d (w)m(alls)g(are)i(assumed)e(t)m(wice)i(di\013eren)m(tiable,)f(strictly) g(monotonic)g(and)g(satisfy)787 4330 y Fo(c)826 4344 y Fm(1)866 4330 y Fk(j)p Fo(x)d Fp(+)1064 4294 y Fn(L)p 1064 4309 V 1070 4361 a Fm(2)1122 4330 y Fk(j)1147 4293 y Fn(m)1209 4302 y Fh(1)1274 4330 y Fk(\024)25 b Fo(U)1432 4345 y Fn(`)1465 4330 y Fp(\()p Fo(x)p Fp(\))h Fk(\024)f Fo(c)1748 4344 y Fm(2)1787 4330 y Fk(j)p Fo(x)c Fp(+)1986 4294 y Fn(L)p 1986 4309 V 1992 4361 a Fm(2)2044 4330 y Fk(j)2069 4293 y Fn(m)2131 4302 y Fh(2)2427 4330 y Fp(for)30 b Fo(x)25 b Fk(\024)g(\000)2820 4294 y Fn(L)p 2820 4309 V 2826 4361 a Fm(2)p Black 3345 4330 a Fp(\(2.3\))p Black 782 4502 a Fo(c)821 4516 y Fm(1)861 4502 y Fk(j)p Fo(x)20 b Fk(\000)1059 4466 y Fn(L)p 1059 4481 V 1065 4533 a Fm(2)1117 4502 y Fk(j)1142 4464 y Fn(m)1204 4473 y Fh(1)1269 4502 y Fk(\024)25 b Fo(U)1427 4516 y Fn(r)1465 4502 y Fp(\()p Fo(x)p Fp(\))h Fk(\024)f Fo(c)1748 4516 y Fm(2)1787 4502 y Fk(j)p Fo(x)c Fk(\000)1986 4466 y Fn(L)p 1986 4481 V 1992 4533 a Fm(2)2044 4502 y Fk(j)2069 4464 y Fn(m)2131 4473 y Fh(2)2427 4502 y Fp(for)30 b Fo(x)25 b Fk(\025)2749 4466 y Fn(L)p 2749 4481 V 2755 4533 a Fm(2)p Black 3345 4502 a Fp(\(2.4\))p Black 128 4713 a(for)35 b(some)i(constan)m(ts)g(0)e Fo(<)g(c)1139 4727 y Fm(1)1213 4713 y Fo(<)f(c)1357 4727 y Fm(2)1432 4713 y Fo(<)g Fk(1)i Fp(and)f(2)h Fk(\024)e Fo(m)2112 4727 y Fm(1)2186 4713 y Fo(<)g(m)2371 4727 y Fm(2)2445 4713 y Fo(<)g Fk(1)p Fp(.)58 b(Moreo)m(v)m(er)38 b Fo(U)3191 4728 y Fn(`)3224 4713 y Fp(\()p Fo(x)p Fp(\))e(=)e(0)128 4860 y(for)41 b Fo(x)j Fk(\025)f(\000)569 4824 y Fn(L)p 569 4839 V 575 4891 a Fm(2)668 4860 y Fp(and)e Fo(U)918 4874 y Fn(r)956 4860 y Fp(\()p Fo(x)p Fp(\))k(=)e(0)f(for)f Fo(x)j Fk(\024)1695 4824 y Fn(L)p 1695 4839 V 1701 4891 a Fm(2)1753 4860 y Fp(.)74 b(W)-8 b(e)42 b(could)f(allo)m(w)g(steep)s (er)g(con\014nemen)m(ts)h(but)128 5007 y(the)30 b(presen)m(t)g(p)s (olynomial)e(conditions)h(turn)g(out)h(to)h(b)s(e)f(tec)m(hnically)f (con)m(v)m(enien)m(t.)42 b(The)30 b(random)128 5154 y(p)s(oten)m(tial) 38 b Fo(V)573 5168 y Fn(!)662 5154 y Fp(consists)g(of)h(a)g(sum)f(of)h (lo)s(cal)f(p)s(erturbations)e(lo)s(cated)j(at)h(the)f(sites)f(of)h(a)g (\014nite)128 5300 y(lattice)30 b(\003)c(=)f Fl(Z)655 5267 y Fm(2)710 5300 y Fk(\\)791 5227 y Fj(\002)829 5300 y Fo(X)i Fk(\002)1022 5227 y Fj(\002)1060 5300 y Fk(\000)1141 5265 y Fn(L)p 1141 5280 V 1147 5332 a Fm(2)1199 5300 y Fo(;)1249 5265 y Fn(L)p 1249 5280 V 1255 5332 a Fm(2)1307 5227 y Fj(\003\003)1413 5300 y Fp(where)j Fo(X)38 b Fp(will)27 b(b)s(e)j(de\014ned)f(latter.)41 b(Th)m(us)815 5512 y Fo(V)868 5526 y Fn(!)919 5512 y Fp(\()p Fo(x;)15 b(y)s Fp(\))26 b(=)1323 5425 y Fj(X)1251 5627 y Fm(\()p Fn(n;m)p Fm(\))p Fi(2)p Fm(\003)1542 5512 y Fo(X)1617 5526 y Fn(n;m)1746 5512 y Fp(\()p Fo(!)s Fp(\))p Fo(V)21 b Fp(\()p Fo(x)f Fk(\000)g Fo(n;)15 b(y)23 b Fk(\000)d Fo(m)p Fp(\))91 b Fo(!)28 b Fk(2)d Fp(\012)500 b(\(2.5\))128 5789 y(where)60 b(the)h(coupling)e(constan)m(ts)j Fo(X)1510 5803 y Fn(n;m)1700 5789 y Fp(are)f(i.i.d.)130 b(random)60 b(v)-5 b(ariables)60 b(with)f(common)128 5935 y(b)s(ounded)31 b(probabilit)m(y)f(densit)m(y) i Fo(h)f Fk(2)e Fo(C)1530 5902 y Fm(2)1569 5935 y Fp(\([)p Fk(\000)p Fp(1)p Fo(;)15 b Fp(1]\).)51 b(The)32 b(lo)s(cal)h(p)s(oten)m (tial)f Fo(V)53 b Fp(satis\014es)33 b Fo(V)50 b Fk(2)29 b Fo(C)3468 5902 y Fm(2)3507 5935 y Fp(,)p Black 1806 6184 a Fd(3)p Black eop %%Page: 4 4 4 3 bop Black Black 128 171 a Fp(0)25 b Fk(\024)g Fo(V)c Fp(\()p Fo(x;)15 b(y)s Fp(\))26 b Fk(\024)f Fo(V)753 185 y Fm(0)817 171 y Fo(<)g Fk(1)p Fp(,)30 b(supp)14 b Fo(V)45 b Fk(\032)25 b Fl(B)1526 97 y Fj(\000)1574 171 y Fq(0)p Fo(;)1676 135 y Fm(1)p 1676 150 36 4 v 1676 202 a(4)1721 97 y Fj(\001)1793 171 y Fp(\(the)30 b(op)s(en)f(ball)f (cen)m(tred)i(at)g(\(0)p Fo(;)15 b Fp(0\))32 b(of)e(radius)3426 135 y Fm(1)p 3426 150 V 3426 202 a(4)3472 171 y Fp(\).)128 317 y(\012)f(=)h([)p Fk(\000)p Fp(1)p Fo(;)15 b Fp(1])575 284 y Fm(\003)662 317 y Fp(is)32 b(the)i(set)f(of)g(all)f(p)s(ossibles) f(realizations,)i(w)m(e)h(will)c(denote)k(b)m(y)f Fl(P)2976 331 y Fm(\003)3062 317 y Fp(the)g(pro)s(duct)128 464 y(measure)d(de\014ned)g(on)g(\012.)41 b(Clearly)29 b(for)h(all)g Fo(!)e Fk(2)e Fp(\012)k(w)m(e)h(ha)m(v)m(e)h Fk(k)p Fo(V)2346 478 y Fn(!)2396 464 y Fk(k)27 b(\024)e Fo(V)2617 478 y Fm(0)2656 464 y Fp(.)42 b(W)-8 b(e)31 b(will)d(assume)j(that)128 611 y Fo(V)181 625 y Fm(0)245 611 y Fk(\034)26 b Fo(B)5 b Fp(,)29 b(that)i(is,)e(w)m(e)i(w)m(ork)f(in)e(a)j(strong)f(magnetic)g (\014eld)f(regime)h(or,)g(equiv)-5 b(alen)m(tly)d(,)29 b(in)g(a)h(w)m(eak)128 758 y(disorder)e(regime.)264 1051 y(Our)c(\014rst)g(result)g(concerns)h(the)h(study)e(of)h Fo(\033)s Fp(\()p Fo(H)1901 1065 y Fn(!)1952 1051 y Fp(\))g(in)f(the)h (energy)h(in)m(terv)-5 b(al)24 b(\001)2949 1065 y Fn(")3011 1051 y Fp(=)h([)p Fo(B)14 b Fp(+)c Fo(";)15 b(B)f Fp(+)128 1198 y Fo(V)181 1212 y Fm(0)220 1198 y Fp(])32 b(that)g(lies)f(inside)e (the)j(\014rst)f(Landau)g(band)g(of)h(the)f(in\014nite)f(bulk)g (system.)45 b(In)31 b(this)f(case)j(the)128 1345 y(in)m(terv)-5 b(al)28 b Fo(X)7 b Fp(,)30 b(that)g(de\014nes)e(the)h(supp)s(ort)f(of)h (the)h(random)e(p)s(oten)m(tial)h(along)g(the)g Fo(x)p Fk(\000)p Fp(direction,)f(is)128 1418 y Fj(\002)166 1492 y Fk(\000)247 1456 y Fn(L)p 247 1471 48 4 v 253 1523 a Fm(2)324 1492 y Fp(+)20 b(log)d Fo(L;)660 1456 y Fn(L)p 660 1471 V 666 1523 a Fm(2)738 1492 y Fk(\000)j Fp(log)d Fo(L)1024 1418 y Fj(\003)1061 1492 y Fp(:)48 b(w)m(e)34 b(lea)m(v)m(e)h(a)f(thin)e(strip)h(of)h(size)f(log)17 b Fo(L)33 b Fp(without)g(random)g(p)s(oten)m(tial)128 1638 y(along)d(eac)m(h)i(con\014ning)d(w)m(all.)264 1785 y(The)21 b(second)g(result)f(is)g(ab)s(out)h Fo(\033)s Fp(\()p Fo(H)1469 1799 y Fn(!)1520 1785 y Fp(\))g(inside)e(the)j (\014rst)e(sp)s(ectral)h(gap)g(of)h(the)f(in\014nite)e(bulk)g(sys-)128 1932 y(tem,)k(more)e(precisely)e(in)g(the)i(energy)g(in)m(terv)-5 b(al)20 b(\001)25 b(=)g(\(2)p Fo(B)5 b Fk(\000)q Fo(\016)n(;)15 b Fp(2)p Fo(B)5 b Fp(+)q Fo(\016)s Fp(\))29 b Fk(\032)c Fp(\()p Fo(B)5 b Fp(+)q Fo(V)2879 1946 y Fm(0)2919 1932 y Fp(+)q Fo(";)15 b Fp(3)p Fo(B)5 b Fk(\000)q Fo(V)3317 1946 y Fm(0)3358 1932 y Fk(\000)q Fo(")p Fp(\).)128 2079 y(In)29 b(this)h(case)h(the)g(random)e(p)s(oten)m(tial)h(\014lls)e(the) j(whole)f(space)h(in)e(b)s(et)m(w)m(een)i(the)f(con\014ning)f(w)m (alls,)128 2226 y(that)i(means)f Fo(X)j Fp(=)807 2152 y Fj(\002)844 2226 y Fk(\000)925 2190 y Fn(L)p 925 2205 V 931 2257 a Fm(2)983 2226 y Fo(;)1033 2190 y Fn(L)p 1033 2205 V 1039 2257 a Fm(2)1091 2152 y Fj(\003)1129 2226 y Fp(.)264 2519 y(Since)g(our)h(system)g(is)g(con\014ned)f(the)i (sp)s(ectrum)e(is)g(made)h(of)h(discrete)f(eigen)m(v)-5 b(alues.)52 b(There)128 2666 y(exists)35 b(a)h(natural)e (classi\014cation)g(of)i(the)g(eigen)m(v)-5 b(alues)35 b(via)g(the)g(quan)m(tum)g(mec)m(hanical)g(curren)m(t)128 2813 y(along)40 b(the)g(p)s(erio)s(dic)e(direction.)69 b(If)40 b Fo( )j Fp(satis\014es)d(the)g(eigen)m(v)-5 b(alue)41 b(equation)f Fo(H)2965 2827 y Fn(!)3015 2813 y Fo( )45 b Fp(=)c Fo(E)5 b( )44 b Fp(the)128 2959 y(curren)m(t)30 b(is)f(de\014ned)g(\(here\))i(as)1554 3106 y Fo(J)1604 3120 y Fn(E)1689 3106 y Fk(\021)25 b Fp(\()p Fo( )s(;)15 b(v)1966 3120 y Fn(y)2009 3106 y Fo( )s Fp(\))1239 b(\(2.6\))128 3284 y(where)39 b Fo(v)444 3298 y Fn(y)527 3284 y Fp(=)i(2\()p Fo(p)765 3298 y Fn(y)834 3284 y Fk(\000)26 b Fo(B)5 b(x)p Fp(\))40 b(is)f(the)i(v)m(elo)s(cit)m(y)f(op)s(erator)g(in)f(the)i Fo(y)s Fk(\000)p Fp(direction.)68 b(Thanks)39 b(to)h Fo(J)3472 3298 y Fn(E)128 3431 y Fp(w)m(e)c(can)g(classify)e(the)i (eigen)m(v)-5 b(alues)35 b(in)f(t)m(w)m(o)j(classes:)51 b(the)36 b(\014rst)f(consists)g(on)h(those)g(whic)m(h)e(ha)m(v)m(e)128 3578 y Fk(j)p Fo(J)203 3592 y Fn(E)263 3578 y Fk(j)i Fo(>)f(C)44 b Fp(with)35 b Fo(C)43 b Fp(a)37 b(p)s(ositiv)m(e)f (constan)m(t)i(uniform)c(in)i Fo(L)p Fp(,)i(the)f(second)g(consists)f (on)g(those)i(for)128 3725 y(whic)m(h)i Fk(j)p Fo(J)474 3739 y Fn(E)535 3725 y Fk(j)45 b Fo(<)f(\017)p Fp(\()p Fo(L)p Fp(\))e(with)f Fo(\017)p Fp(\()p Fo(L)p Fp(\))k Fk(!)g Fp(0)d(as)h Fo(L)h Fk(!)h(1)d Fp(\(w)m(e)h(stress)f(that)g(here) g Fo(L)g Fp(is)f(\014nite)g(but)128 3872 y(macroscopic,)33 b(the)f(limit)e(means)j(that)f Fo(\017)p Fp(\()p Fo(L)p Fp(\))h(is)e(in\014nitesimally)d(small)j(with)g Fo(L)p Fp(\).)46 b(The)32 b(ph)m(ysical)128 4018 y(meaning)d(of)i(this)e (classi\014cation)g(is)h(brie\015y)e(discussed)h(at)i(the)g(end)e(of)i (section)f(3.)264 4312 y(The)24 b(main)g(idea)g(of)h(our)f(approac)m(h) h(is)e(to)j(\014rst)e(lo)s(ok)g(at)h(some)g(easier)g(Hamiltonians)e (and)h(then)128 4459 y(link)31 b(them)i(together)h(to)g(get)h(prop)s (erties)c(on)i(the)h(full)d(Hamiltonian)g Fo(H)2657 4473 y Fn(!)2707 4459 y Fp(.)49 b(In)32 b(what)i(follo)m(ws)e(w)m(e)128 4605 y(do)c(not)i(analyze)f(these)g(easier)g(Hamiltonians)e(but)h(w)m (e)i(just)e(in)m(tro)s(duce)g(the)h(minimal)d(notations)128 4752 y(and)j(prop)s(erties)g(\(see)j([FM1)q(])e(and)g([FM2)r(])g(for)g (the)h(details\).)128 5120 y Fg(3)161 b(Main)55 b(results)128 5356 y Fp(F)-8 b(or)31 b(the)f(analysis)f(of)i Fo(\033)s Fp(\()p Fo(H)1059 5370 y Fn(!)1109 5356 y Fp(\))g(in)e(\001)1357 5370 y Fn(")1424 5356 y Fp(w)m(e)i(need)f(to)h(kno)m(w)f(some)h(prop)s (erties)e(of)h(the)h(Hamiltonian)1296 5549 y Fo(H)1379 5512 y Fm(0)1372 5572 y Fn(\013)1447 5549 y Fp(=)25 b Fo(H)1619 5563 y Fm(0)1678 5549 y Fp(+)20 b Fo(U)1831 5563 y Fn(\013)2062 5549 y Fo(\013)26 b Fp(=)f Fo(`;)15 b(r)984 b Fp(\(3.1\))128 5742 y(called)29 b Fc(pur)-5 b(e)34 b(e)-5 b(dge)32 b(Hamiltonian)p Fp(.)43 b(Its)30 b(sp)s(ectrum)f(is)h(giv)m(en)g(b)m(y)1199 5935 y Fo(\033)s Fp(\()p Fo(H)1372 5898 y Fm(0)1365 5958 y Fn(\013)1414 5935 y Fp(\))c(=)1571 5862 y Fj(\010)1624 5935 y Fo(E)1696 5898 y Fn(\013)1691 5958 y(nk)1776 5935 y Fp(;)15 b Fo(n)26 b Fk(2)e Fl(N)7 b Fo(;)15 b(k)35 b Fk(2)2260 5899 y Fm(2)p Fn(\031)p 2260 5914 79 4 v 2275 5967 a(L)2348 5935 y Fl(Z)2413 5862 y Fj(\011)3345 5935 y Fp(\(3.2\))p Black 1806 6184 a Fd(4)p Black eop %%Page: 5 5 5 4 bop Black Black Black Black Black 476 1469 a @beginspecial 0 @llx 0 @lly 326 @urx 169 @ury 3260 @rwi @setspecial %%BeginDocument: specH0.pstex %!PS-Adobe-2.0 EPSF-2.0 %%Title: specH0.pstex %%Creator: fig2dev Version 3.2 Patchlevel 3c %%CreationDate: Wed Feb 6 08:45:36 2002 %%For: ferrari@iptdec1.epfl.ch (Christian Ferrari) %%BoundingBox: 0 0 326 169 %%Magnification: 0.6000 %%EndComments /$F2psDict 200 dict def $F2psDict begin $F2psDict /mtrx matrix put /col-1 {0 setgray} bind def /col0 {0.000 0.000 0.000 srgb} bind def /col1 {0.000 0.000 1.000 srgb} bind def /col2 {0.000 1.000 0.000 srgb} bind def /col3 {0.000 1.000 1.000 srgb} bind def /col4 {1.000 0.000 0.000 srgb} bind def /col5 {1.000 0.000 1.000 srgb} bind def /col6 {1.000 1.000 0.000 srgb} bind def /col7 {1.000 1.000 1.000 srgb} bind def /col8 {0.000 0.000 0.560 srgb} bind def /col9 {0.000 0.000 0.690 srgb} bind def /col10 {0.000 0.000 0.820 srgb} bind def /col11 {0.530 0.810 1.000 srgb} bind def /col12 {0.000 0.560 0.000 srgb} bind def /col13 {0.000 0.690 0.000 srgb} bind def /col14 {0.000 0.820 0.000 srgb} bind def /col15 {0.000 0.560 0.560 srgb} bind def /col16 {0.000 0.690 0.690 srgb} bind def /col17 {0.000 0.820 0.820 srgb} bind def /col18 {0.560 0.000 0.000 srgb} bind def /col19 {0.690 0.000 0.000 srgb} bind def /col20 {0.820 0.000 0.000 srgb} bind def /col21 {0.560 0.000 0.560 srgb} bind def /col22 {0.690 0.000 0.690 srgb} bind def /col23 {0.820 0.000 0.820 srgb} bind def /col24 {0.500 0.190 0.000 srgb} bind def /col25 {0.630 0.250 0.000 srgb} bind def /col26 {0.750 0.380 0.000 srgb} bind def /col27 {1.000 0.500 0.500 srgb} bind def /col28 {1.000 0.630 0.630 srgb} bind def /col29 {1.000 0.750 0.750 srgb} bind def /col30 {1.000 0.880 0.880 srgb} bind def /col31 {1.000 0.840 0.000 srgb} bind def end save newpath 0 169 moveto 0 0 lineto 326 0 lineto 326 169 lineto closepath clip newpath -42.0 224.0 translate 1 -1 scale /cp {closepath} bind def /ef {eofill} bind def /gr {grestore} bind def /gs {gsave} bind def /sa {save} bind def /rs {restore} bind def /l {lineto} bind def /m {moveto} bind def /rm {rmoveto} bind def /n {newpath} bind def /s {stroke} bind def /sh {show} bind def /slc {setlinecap} bind def /slj {setlinejoin} bind def /slw {setlinewidth} bind def /srgb {setrgbcolor} bind def /rot {rotate} bind def /sc {scale} bind def /sd {setdash} bind def /ff {findfont} bind def /sf {setfont} bind def /scf {scalefont} bind def /sw {stringwidth} bind def /tr {translate} bind def /tnt {dup dup currentrgbcolor 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add 4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb} bind def /shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul 4 -2 roll mul srgb} bind def /DrawEllipse { /endangle exch def /startangle exch def /yrad exch def /xrad exch def /y exch def /x exch def /savematrix mtrx currentmatrix def x y tr xrad yrad sc 0 0 1 startangle endangle arc closepath savematrix setmatrix } def /$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def /$F2psEnd {$F2psEnteredState restore end} def $F2psBegin %%Page: 1 1 10 setmiterlimit 0.03600 0.03600 sc % % Fig objects follow % 7.500 slw % Ellipse n 3900 3375 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 3300 2925 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 2700 2400 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 5100 3825 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 5700 3975 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 6300 4050 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 6900 4125 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 7500 4200 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 8100 4275 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 8700 4350 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 9300 4425 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 9900 4425 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 4500 4425 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 3900 4200 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 3300 3750 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 2700 3225 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 2100 2400 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 1500 1575 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 4500 3600 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 5100 4650 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 5700 4800 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 6300 4875 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 6900 4950 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 7500 5025 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 8100 5100 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 8700 5175 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 9300 5250 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 9900 5250 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Ellipse n 2100 1725 20 20 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr % Polyline gs clippath 10215 5730 m 10215 5670 l 10030 5670 l 10180 5700 l 10030 5730 l cp eoclip n 1200 5700 m 10200 5700 l gs col0 s gr gr % arrowhead n 10030 5730 m 10180 5700 l 10030 5670 l 10060 5700 l 10030 5730 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 5730 1785 m 5670 1785 l 5670 1970 l 5700 1820 l 5730 1970 l cp eoclip n 5700 1800 m 5700 5775 l gs col0 s gr gr % arrowhead n 5730 1970 m 5700 1820 l 5670 1970 l 5700 1940 l 5730 1970 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 2655 3314 m 2617 3267 l 2473 3382 l 2609 3312 l 2510 3429 l cp eoclip n 2100 3600 m 2325 3450 l 2250 3600 l 2625 3300 l gs col0 s gr gr % arrowhead n 2510 3429 m 2609 3312 l 2473 3382 l 2515 3386 l 2510 3429 l cp gs 0.00 setgray ef gr col0 s % Polyline gs clippath 3270 2790 m 3330 2790 l 3330 2605 l 3300 2755 l 3270 2605 l cp eoclip n 3300 2325 m 3300 2775 l gs col0 s gr gr % arrowhead n 3270 2605 m 3300 2755 l 3330 2605 l 3300 2635 l 3270 2605 l cp gs 0.00 setgray ef gr col0 s $F2psEnd rs %%EndDocument @endspecial 0 0 0 TeXcolorrgb 638 754 a Fo(E)710 721 y Fn(`)705 782 y Fm(0)p Fn(k)p Black 0 0 0 TeXcolorrgb 3122 1416 a Fm(2)p Fn(\031)p 3122 1431 79 4 v 3137 1483 a(L)3211 1451 y Fl(Z)p Black 0 0 0 TeXcolorrgb 3157 1204 a Fo(B)p Black 0 0 0 TeXcolorrgb 1065 259 a(E)1137 226 y Fn(`)1132 287 y Fm(1)p Fn(k)p Black 0 0 0 TeXcolorrgb 3157 957 a Fp(3)p Fo(B)p Black -116 1798 a Fd(Figure)29 b(2:)42 b Fc(The)31 b(sp)-5 b(e)g(ctrum)33 b(of)e Fo(H)1060 1765 y Fm(0)1053 1826 y Fn(`)1130 1798 y Fc(lies)g(on)g(monotonic)i(de) -5 b(cr)g(e)g(asing)32 b(br)-5 b(anches.)43 b(That)32 b(of)f Fo(H)3114 1765 y Fm(0)3107 1821 y Fn(r)3184 1798 y Fc(lies)g(on)g(similar,)-116 1945 y(but)h(monotonic)j(incr)-5 b(e)g(asing,)34 b(br)-5 b(anches.)44 b(The)34 b(sp)-5 b(e)g(ctr)g(al)35 b(br)-5 b(anches)34 b(ar)-5 b(e)34 b(given)f(by)f(the)i(disp)-5 b(ersion)35 b(r)-5 b(elation)35 b(for)-116 2092 y Fo(L)25 b Fp(=)g Fk(1)p Fc(.)p Black 264 2320 a Fp(The)c(quan)m(tum)f(mec)m(hanical)h(curren)m(ts)g(asso)s (ciated)h(to)g(the)f(eigenfunctions)f Fo( )2937 2287 y Fn(\013)2934 2348 y(nk)3041 2320 y Fp(whose)h(eigen-)128 2467 y(v)-5 b(alue)30 b(is)f(in)g(\001)636 2481 y Fn(")703 2467 y Fp(\(w)m(e)i(ha)m(v)m(e)h Fo(n)24 b Fp(=)h(0\))31 b(satisfy)1323 2701 y Fk(j)p Fo(J)1407 2663 y Fn(\013)1398 2724 y Fm(0)p Fn(k)1477 2701 y Fk(j)25 b Fp(=)g Fk(j)p Fp(\()p Fo( )1745 2663 y Fn(\013)1742 2724 y Fm(0)p Fn(k)1821 2701 y Fo(;)15 b(v)1905 2715 y Fn(y)1947 2701 y Fo( )2009 2663 y Fn(\013)2006 2724 y Fm(0)p Fn(k)2084 2701 y Fp(\))p Fk(j)26 b Fo(>)f(C)1014 b Fp(\(3.3\))128 2935 y(with)33 b Fo(C)38 b(>)31 b Fp(0)j(a)h(n)m(umerical)e(constan)m(t)i(indep)s (enden)m(t)d(of)i Fo(L)g Fp([FM1)r(].)52 b(Moreo)m(v)m(er)36 b(w)m(e)f(will)d(assume)128 3082 y(the)e(follo)m(wing)p Black 128 3300 a Fq(Hyp)s(othesis)35 b(1.)p Black 42 w Fc(Fix)e Fo(")25 b(>)g Fp(0)p Fc(.)42 b(Ther)-5 b(e)34 b(exist)f Fo(L)p Fp(\()p Fo(")p Fp(\))g Fc(and)h Fo(d)p Fp(\()p Fo(")p Fp(\))26 b Fo(>)f Fp(0)33 b Fc(such)g(that)h(for)f(al)5 b(l)33 b Fo(L)25 b(>)g(L)p Fp(\()p Fo(")p Fp(\))1049 3548 y(dist)1211 3474 y Fj(\000)1253 3548 y Fo(\033)s Fp(\()p Fo(H)1426 3510 y Fm(0)1419 3571 y Fn(`)1466 3548 y Fp(\))c Fk(\\)e Fp(\001)1678 3562 y Fn(")1715 3548 y Fo(;)c(\033)s Fp(\()p Fo(H)1928 3510 y Fm(0)1921 3570 y Fn(r)1968 3548 y Fp(\))21 b Fk(\\)f Fp(\001)2181 3562 y Fn(")2217 3474 y Fj(\001)2284 3548 y Fk(\025)2390 3486 y Fo(d)p Fp(\()p Fo(")p Fp(\))p 2390 3527 161 4 v 2439 3610 a Fo(L)2586 3548 y(:)734 b Fp(\(3.4\))128 3782 y(This)20 b(h)m(yp)s(othesis)g(is)h(imp)s(ortan)m(t)g(b)s(ecause)h(a)g(minimal)d (amoun)m(t)k(of)f(non-degeneracy)h(b)s(et)m(w)m(een)f(the)128 3928 y(sp)s(ectra)28 b(of)h(the)f(t)m(w)m(o)i(edge)f(systems)g(is)e (needed)h(in)g(order)g(to)h(con)m(trol)g(bac)m(kscattering)g(e\013ects) h(in-)128 4075 y(duced)22 b(b)m(y)g(the)h(random)g(p)s(oten)m(tial.)37 b(Indeed)22 b(in)g(a)h(system)g(with)e(t)m(w)m(o)k(b)s(oundaries)20 b(bac)m(kscattering)128 4222 y(fa)m(v)m(ors)32 b(lo)s(calization)e(and) h(has)g(a)h(tendency)f(to)h(destro)m(y)g(curren)m(ts.)43 b(Remark)32 b(that)g(this)e(h)m(yp)s(oth-)128 4369 y(esis)e(can)i(b)s (e)f(v)m(eri\014ed)f(b)m(y)i(taking)f(t)m(w)m(o)i(symmetric)e (con\014ning)e(p)s(oten)m(tials)i Fo(U)2786 4384 y Fn(`)2819 4369 y Fp(\()p Fo(x)p Fp(\))d(=)f Fo(U)3125 4383 y Fn(r)3163 4369 y Fp(\()p Fk(\000)p Fo(x)p Fp(\))30 b(and)128 4515 y(adding)36 b(a)i(suitable)e(\015ux)g(line)g(along)h(the)h(cylinder)d (axes)j(\(see)h(in)d(particular)g(App)s(endix)f(C)i(in)128 4662 y([FM2)q(]\).)264 4809 y(W)-8 b(e)32 b(also)e(need)g(to)h(kno)m(w) g(some)f(prop)s(erties)f(of)i(the)f Fc(bulk)i(Hamiltonian)1524 5043 y Fo(H)1600 5058 y Fn(b)1660 5043 y Fp(=)25 b Fo(H)1832 5057 y Fm(0)1891 5043 y Fp(+)20 b Fo(V)2035 5057 y Fn(!)2110 5043 y Fo(:)1210 b Fp(\(3.5\))128 5277 y(Its)20 b(essen)m(tial)h(sp)s (ectrum)f(is)f(giv)m(en)i(b)m(y)g(the)g(Landau)f(lev)m(els)g(and)h(the) g(whole)f(sp)s(ectrum)f(is)h(con)m(tained)128 5424 y(in)i(the)i(Landau) f(bands)g Fo(\033)s Fp(\()p Fo(H)1123 5439 y Fn(b)1158 5424 y Fp(\))i Fk(\032)1314 5356 y Fj(S)1390 5451 y Fn(n)p Fi(\025)p Fm(0)1542 5424 y Fp([\(2)p Fo(n)c Fp(+)f(1\))p Fo(B)25 b Fk(\000)20 b Fo(V)2132 5438 y Fm(0)2172 5424 y Fo(;)15 b Fp(\(2)p Fo(n)21 b Fp(+)f(1\))p Fo(B)25 b Fp(+)20 b Fo(V)2777 5438 y Fm(0)2817 5424 y Fp(].)38 b(W)-8 b(e)25 b(will)d(supp)s(ose)128 5570 y(that)31 b(the)f(\(discrete\))h(sp)s(ectrum)e(in)g(\001)1465 5584 y Fn(")1532 5570 y Fp(full\014lls)d(the)p Black 128 5789 a Fq(Hyp)s(othesis)37 b(2.)p Black 42 w Fc(Fix)d(any)h Fo(")28 b(>)f Fp(0)p Fc(.)46 b(Ther)-5 b(e)35 b(exist)f Fo(\026)p Fp(\()p Fo(")p Fp(\))h Fc(a)f(strictly)h(p)-5 b(ositive)35 b(c)-5 b(onstant)36 b(and)e Fo(L)p Fp(\()p Fo(")p Fp(\))128 5935 y Fc(such)j(that)i(for)f(al)5 b(l)38 b Fo(L)d(>)f(L)p Fp(\()p Fo(")p Fp(\))k Fc(one)g(c)-5 b(an)38 b(\014nd)g(a)g(set)g(of)g(r)-5 b(e)g(alizations)40 b(of)e(the)g(r)-5 b(andom)40 b(p)-5 b(otential)p Black 1806 6184 a Fd(5)p Black eop %%Page: 6 6 6 5 bop Black Black 128 171 a Fp(\012)194 114 y Fb(0)260 171 y Fc(with)42 b Fl(P)521 185 y Fm(\003)575 171 y Fp(\(\012)676 114 y Fb(0)702 171 y Fp(\))e Fk(\025)g Fp(1)27 b Fk(\000)e Fo(L)1118 138 y Fi(\000)p Fn(\022)1212 171 y Fc(,)43 b Fo(\022)f(>)d Fp(0)p Fc(,)k(with)f(the)f(pr)-5 b(op)g(erty)43 b(that)f(if)f Fo(!)h Fk(2)e Fp(\012)2879 114 y Fb(0)2946 171 y Fc(the)h(eigenstates)128 317 y(c)-5 b(orr)g(esp)g(onding)35 b(to)f Fo(E)883 284 y Fn(b)878 345 y(\014)950 317 y Fk(2)25 b Fo(\033)s Fp(\()p Fo(H)1202 332 y Fn(b)1237 317 y Fp(\))20 b Fk(\\)g Fp(\001)1449 331 y Fn(")1518 317 y Fc(satisfy)767 549 y Fk(j)p Fo( )854 511 y Fn(b)851 572 y(\014)899 549 y Fp(\()p Fo(x;)i Fp(\026)-52 b Fo(y)1071 564 y Fn(\014)1118 549 y Fp(\))p Fk(j)26 b(\024)f Fo(e)1342 511 y Fi(\000)p Fn(\026)p Fm(\()p Fn(")p Fm(\))p Fn(L)1765 549 y Fo(;)201 b Fk(j)p Fo(@)2064 563 y Fn(y)2106 549 y Fo( )2168 511 y Fn(b)2165 572 y(\014)2213 549 y Fp(\()p Fo(x;)21 b Fp(\026)-51 b Fo(y)2385 564 y Fn(\014)2432 549 y Fp(\))p Fk(j)26 b(\024)f Fo(e)2656 511 y Fi(\000)p Fn(\026)p Fm(\()p Fn(")p Fm(\))p Fn(L)3345 549 y Fp(\(3.6\))128 781 y Fc(for)33 b(some)39 b Fp(\026)-51 b Fo(y)550 796 y Fn(\014)629 781 y Fc(dep)-5 b(ending)34 b(on)f Fo(!)j Fc(and)d Fo(L)p Fc(.)128 997 y Fp(Since)25 b Fo(V)414 1011 y Fn(!)491 997 y Fp(is)g(random)h(w)m(e)h(exp)s(ect)g(that)g (eigenfunctions)e(with)g(energies)i(in)e(\001)2827 1011 y Fn(")2890 997 y Fp(\(not)i(to)s(o)g(close)g(to)128 1144 y(the)d(Landau)f(lev)m(els)h(where)g(the)g(lo)s(calization)f (length)h(div)m(erges\))g(are)h(exp)s(onen)m(tially)d(lo)s(calized)h (on)128 1290 y(a)g(scale)g Fk(O)s Fp(\(1\))i(with)c(resp)s(ect)i(to)h Fo(L)p Fp(.)38 b(Inequalities)21 b(\(3.6\))k(are)f(a)f(w)m(eak)m(er)h (v)m(ersion)f(of)g(this)f(statemen)m(t,)128 1437 y(and)i(ha)m(v)m(e)h (b)s(een)f(c)m(hec)m(k)m(ed)j(for)d(the)h(sp)s(ecial)e(case)i(where)f (the)h(random)f(p)s(oten)m(tial)g(is)g(a)g(sum)g(of)h(rank)128 1584 y(one)34 b(p)s(erturbations)e([FM3)q(])i(using)f(the)h(metho)s(ds) g(of)g(Aizenman)f(and)h(Molc)m(hano)m(v)h([AM)q(].)52 b(The)128 1731 y(main)33 b(consequence)j(of)f(Hyp)s(othesis)f(2)h(is)f (that)h(a)h(state)g(satisfying)f(\(3.6\))h(do)s(es)f(not)g(carry)g(an)m (y)128 1878 y(appreciable)29 b(curren)m(t)h(\(con)m(trary)h(to)g(the)g (eigenstates)h(of)e Fo(H)2238 1845 y Fm(0)2231 1900 y Fn(\013)2280 1878 y Fp(\))h(in)e(the)i(sense)f(that)1184 2109 y Fo(J)1243 2072 y Fn(b)1234 2132 y(\014)1306 2109 y Fp(=)25 b(\()p Fo( )1499 2072 y Fn(b)1496 2132 y(\014)1544 2109 y Fo(;)15 b(v)1628 2123 y Fn(y)1670 2109 y Fo( )1732 2072 y Fn(b)1729 2132 y(\014)1776 2109 y Fp(\))26 b(=)f Fk(O)2023 2008 y Fj(\020)2077 2109 y Fo(e)2119 2072 y Fi(\000)p Fn(\026)p Fm(\()p Fn(")p Fm(\))p Fn(L)2357 2008 y Fj(\021)2451 2109 y Fo(:)869 b Fp(\(3.7\))264 2341 y(W)-8 b(e)36 b(are)f(no)m(w)f(ready)h(to)g(state)h(our)e(\014rst) g(result)g(on)g(the)h(eigen)m(v)-5 b(alues)35 b(lying)e(in)g(\001)3168 2355 y Fn(")3237 2341 y Fp(=)f([)p Fo(B)c Fp(+)128 2488 y Fo(";)15 b(B)25 b Fp(+)20 b Fo(V)448 2502 y Fm(0)488 2488 y Fp(].)p Black 128 2704 a Fq(Theorem)k(1.)p Black 35 w Fc(Fix)h Fo(")h(>)f Fp(0)g Fc(and)h(assume)f(that)i Fp(\()p Fo(H)7 b Fp(1\))26 b Fc(and)f Fp(\()p Fo(H)7 b Fp(2\))26 b Fc(ar)-5 b(e)26 b(ful\014l)5 b(le)-5 b(d.)40 b(Assume)25 b Fo(B)30 b(>)25 b Fp(4)p Fo(V)3465 2718 y Fm(0)3504 2704 y Fc(.)128 2851 y(Then)45 b(ther)-5 b(e)45 b(exists)g(a)h(numeric)-5 b(al)45 b(c)-5 b(onstant)47 b Fo(\015)52 b(>)47 b Fp(0)e Fc(and)h(an)2425 2828 y Fp(\026)2414 2851 y Fo(L)h Fk(\025)g Fo(L)p Fp(\()p Fo(")p Fp(\))f Fc(such)e(that)i(for)g(al)5 b(l)128 2997 y Fo(L)47 b(>)365 2974 y Fp(\026)354 2997 y Fo(L)e Fc(one)g(c)-5 b(an)45 b(\014nd)g(a)g(set)1272 2974 y Fp(^)1262 2997 y(\012)h Fk(\032)h Fp(\012)d Fc(of)h(r)-5 b(e)g(alizations)48 b(of)d(the)g(r)-5 b(andom)47 b(p)-5 b(otential)46 b Fo(V)3272 3011 y Fn(!)3367 2997 y Fc(with)128 3144 y Fl(P)183 3158 y Fm(\003)236 3144 y Fp(\()281 3121 y(^)271 3144 y(\012\))30 b Fk(\025)e Fp(1)22 b Fk(\000)g Fo(L)723 3111 y Fi(\000)p Fn(s)849 3144 y Fp(\()p Fo(s)29 b Fk(\035)g Fp(1\))35 b Fc(such)g(that)h(for)f(any)g Fo(!)d Fk(2)2100 3121 y Fp(^)2090 3144 y(\012)p Fc(,)i Fo(\033)s Fp(\()p Fo(H)2384 3158 y Fn(!)2435 3144 y Fp(\))22 b Fk(\\)f Fp(\001)2650 3158 y Fn(")2721 3144 y Fc(is)35 b(the)g(union)g(of)g(thr)-5 b(e)g(e)128 3291 y(sets)43 b Fp(\006)383 3306 y Fn(`)444 3291 y Fk([)27 b Fp(\006)598 3306 y Fn(b)660 3291 y Fk([)h Fp(\006)815 3305 y Fn(r)853 3291 y Fc(,)45 b(e)-5 b(ach)45 b(dep)-5 b(ending)44 b(on)g Fo(!)i Fc(and)e Fo(L)p Fc(,)i(and)e(char)-5 b(acterize)g(d)46 b(by)d(the)h(fol)5 b(lowing)128 3438 y(pr)-5 b(op)g(erties:)p Black 210 3625 a(a\))p Black 49 w Fk(E)398 3592 y Fn(\013)390 3653 y(k)473 3625 y Fk(2)25 b Fp(\006)625 3639 y Fn(\013)707 3625 y Fp(\()p Fo(\013)h Fp(=)f Fo(`;)15 b(r)s Fp(\))32 b Fc(ar)-5 b(e)34 b(a)f(smal)5 b(l)33 b(p)-5 b(erturb)g(ation)36 b(of)c Fo(E)2276 3592 y Fn(\013)2271 3653 y Fm(0)p Fn(k)2375 3625 y Fk(2)25 b Fo(\033)s Fp(\()p Fo(H)2634 3592 y Fm(0)2627 3647 y Fn(\013)2676 3625 y Fp(\))c Fk(\\)f Fp(\001)2889 3639 y Fn(")2958 3625 y Fc(with)1069 3857 y Fk(jE)1150 3819 y Fn(\013)1142 3880 y(k)1220 3857 y Fk(\000)g Fo(E)1383 3819 y Fn(\013)1378 3880 y Fm(0)p Fn(k)1456 3857 y Fk(j)26 b(\024)f Fo(e)1645 3819 y Fi(\000)p Fn(\015)t(B)s Fm(\(log)14 b Fn(L)p Fm(\))2002 3796 y Fh(2)2041 3857 y Fo(;)387 b(\013)26 b Fp(=)f Fo(`;)15 b(r)28 b(:)540 b Fp(\(3.8\))p Black 214 4108 a Fc(b\))p Black 49 w(F)-7 b(or)34 b Fk(E)568 4075 y Fn(\013)560 4136 y(k)643 4108 y Fk(2)25 b Fp(\006)795 4122 y Fn(\013)876 4108 y Fc(the)33 b(curr)-5 b(ent)34 b Fk(J)1424 4075 y Fn(\013)1408 4136 y(k)1506 4108 y Fc(of)f(the)g(asso)-5 b(ciate)g(d)35 b(eigenstate)e(satis\014es)1066 4340 y Fk(j)q(J)1170 4302 y Fn(\013)1154 4363 y(k)1240 4340 y Fk(\000)20 b Fo(J)1390 4302 y Fn(\013)1381 4363 y Fm(0)p Fn(k)1459 4340 y Fk(j)26 b(\024)f Fo(e)1648 4302 y Fi(\000)p Fn(\015)t(B)s Fm(\(log)14 b Fn(L)p Fm(\))2005 4279 y Fh(2)2044 4340 y Fo(;)387 b(\013)26 b Fp(=)f Fo(`;)15 b(r)28 b(:)537 b Fp(\(3.9\))p Black 214 4591 a Fc(c\))p Black 49 w Fp(\006)408 4606 y Fn(b)475 4591 y Fc(c)-5 b(ontains)34 b(the)f(same)g(numb)-5 b(er)33 b(of)g(ener)-5 b(gy)33 b(levels)g(as)g Fo(\033)s Fp(\()p Fo(H)2460 4606 y Fn(b)2494 4591 y Fp(\))21 b Fk(\\)f Fp(\001)2707 4605 y Fn(")2776 4591 y Fc(and)33 b Fp(\()p Fo(p)26 b Fk(\035)f Fp(1\))1180 4823 y(dist)o(\(\006)1428 4838 y Fn(b)1462 4823 y Fo(;)15 b Fp(\006)1568 4837 y Fn(\013)1618 4823 y Fp(\))25 b Fk(\025)g Fo(L)1836 4785 y Fi(\000)p Fn(p)1931 4823 y Fo(;)387 b(\013)26 b Fp(=)e Fo(`;)15 b(r)29 b(:)605 b Fp(\(3.10\))p Black 210 5074 a Fc(d\))p Black 49 w(The)33 b(curr)-5 b(ent)33 b(asso)-5 b(ciate)g(d)36 b(to)d(e)-5 b(ach)33 b(level)g Fk(E)1838 5089 y Fn(\014)1910 5074 y Fk(2)25 b Fp(\006)2062 5089 y Fn(b)2128 5074 y Fc(satis\014es)1553 5306 y Fk(jJ)1640 5321 y Fn(\014)1687 5306 y Fk(j)g(\024)g Fo(e)1875 5268 y Fi(\000)p Fn(\015)t(B)s Fm(\(log)14 b Fn(L)p Fm(\))2232 5245 y Fh(2)2297 5306 y Fo(:)978 b Fp(\(3.11\))264 5557 y(W)-8 b(e)32 b(no)m(w)f(turn)f(to)i(the)g(c)m (haracterisation)f(of)h(eigen)m(v)-5 b(alues)31 b(lying)e(in)h(\001)c (=)g(\(2)p Fo(B)g Fk(\000)21 b Fo(\016)n(;)15 b Fp(2)p Fo(B)26 b Fp(+)21 b Fo(\016)s Fp(\).)128 5704 y(In)29 b(this)h(case)h(the)g(\014rst)e(easier)h(Hamiltonian)f(is)1179 5935 y Fo(H)1255 5949 y Fn(\013)1330 5935 y Fp(=)c Fo(H)1502 5949 y Fm(0)1561 5935 y Fp(+)20 b Fo(U)1714 5949 y Fn(\013)1784 5935 y Fp(+)f Fo(V)1948 5898 y Fn(\013)1927 5958 y(!)2179 5935 y Fo(\013)26 b Fp(=)f Fo(`;)15 b(r)822 b Fp(\(3.12\))p Black 1806 6184 a Fd(6)p Black eop %%Page: 7 7 7 6 bop Black Black 128 171 a Fp(called)51 b Fc(r)-5 b(andom)55 b(e)-5 b(dge)53 b(Hamiltonian)p Fp(.)107 b(In)52 b(\(3.12\))i(the)e(random)f(p)s(oten)m(tial)h Fo(V)3033 138 y Fn(\013)3013 193 y(!)3135 171 y Fp(is)f(the)h(re-)128 317 y(striction)d(of)j Fo(V)685 331 y Fn(!)786 317 y Fp(to)f(\003)980 331 y Fn(\013)1089 317 y Fk(\032)60 b Fp(\003,)c(where)50 b(\003)1710 331 y Fn(\013)1811 317 y Fp(is)g(a)h(strip)e(of)i(size)2569 240 y Fk(p)p 2645 240 62 4 v 77 x Fo(L)f Fp(in)g(the)h Fo(x)p Fk(\000)p Fp(direction)128 464 y(along)41 b(the)h(con\014ning)e(w)m(alls:)63 b(\003)1296 478 y Fn(r)1378 464 y Fp(=)43 b Fl(Z)1557 431 y Fm(2)1620 464 y Fk(\\)1709 363 y Fj(h)1751 464 y Fp([)1786 428 y Fn(L)p 1786 443 48 4 v 1792 496 a Fm(2)1865 464 y Fk(\000)1966 428 y Fm(3)2001 372 y Fi(p)p 2060 372 48 3 v 56 x Fn(L)p 1966 443 143 4 v 2019 496 a Fm(4)2138 464 y Fk(\000)20 b Fp(1)p Fo(;)2325 428 y Fn(L)p 2325 443 48 4 v 2331 496 a Fm(2)2383 464 y Fp(])g Fk(\002)g Fp([)p Fk(\000)2625 428 y Fn(L)p 2625 443 V 2631 496 a Fm(2)2683 464 y Fo(;)2733 428 y Fn(L)p 2733 443 V 2739 496 a Fm(2)2791 464 y Fp(])2816 363 y Fj(i)2901 464 y Fp(and)41 b(\003)3152 479 y Fn(`)3229 464 y Fp(=)j Fl(Z)3409 431 y Fm(2)3472 464 y Fk(\\)128 535 y Fj(h)171 636 y Fp([)p Fk(\000)277 600 y Fn(L)p 277 615 V 283 667 a Fm(2)334 636 y Fo(;)15 b Fk(\000)455 600 y Fn(L)p 455 615 V 461 667 a Fm(2)534 636 y Fp(+)635 600 y Fm(3)670 544 y Fi(p)p 729 544 48 3 v 56 x Fn(L)p 635 615 143 4 v 688 667 a Fm(4)807 636 y Fp(+)20 b(1])h Fk(\002)f Fp([)p Fk(\000)1186 600 y Fn(L)p 1186 615 48 4 v 1192 667 a Fm(2)1243 636 y Fo(;)1294 600 y Fn(L)p 1294 615 V 1300 667 a Fm(2)1352 636 y Fp(])1377 535 y Fj(i)1420 636 y Fp(.)41 b(The)29 b(sp)s(ectrum)h(of)g Fo(H)2249 650 y Fn(\013)2329 636 y Fp(is)f(giv)m(en)h(b)m(y)1405 859 y Fo(\033)s Fp(\()p Fo(H)1571 873 y Fn(\013)1621 859 y Fp(\))c(=)e Fk(f)q Fo(E)1895 822 y Fn(\013)1890 882 y(\024)1945 859 y Fp(;)15 b Fo(\024)26 b Fk(2)f Fl(Z)p Fk(g)1041 b Fp(\(3.13\))128 1082 y(and)33 b Fo(E)380 1049 y Fn(\013)375 1105 y(\024)464 1082 y Fp(are)h(isolated)f(eigen)m(v)-5 b(alues)34 b(with)f(accum)m (ulation)g(p)s(oin)m(ts)g(at)i(the)f(Landau)f(lev)m(els.)51 b(The)128 1229 y(quan)m(tum)29 b(mec)m(hanical)i(curren)m(ts)f Fo(J)1390 1196 y Fn(\013)1381 1252 y(\024)1470 1229 y Fp(asso)s(ciated)g(to)i(the)e(energies)g(in)f(\001)h(satisfy)1346 1452 y Fk(j)p Fo(J)1430 1415 y Fn(\013)1421 1475 y(\024)1480 1452 y Fk(j)c Fp(=)f Fk(j)p Fp(\()p Fo( )1749 1415 y Fn(\013)1746 1475 y(\024)1799 1452 y Fo(;)15 b(v)1883 1466 y Fn(y)1925 1452 y Fo( )1987 1415 y Fn(\013)1984 1475 y(\024)2037 1452 y Fp(\))p Fk(j)26 b Fo(>)f(C)2291 1415 y Fi(0)3300 1452 y Fp(\(3.14\))128 1676 y(with)31 b Fo(C)409 1643 y Fi(0)461 1676 y Fo(>)e Fp(0)k(a)h(n)m(umerical)d (constan)m(t)j(indep)s(enden)m(t)d(of)i Fo(L)f Fp([FM2)r(].)48 b(By)33 b(the)g(w)m(a)m(y)h(remark)e(that,)128 1822 y(since)38 b(the)h(random)g(v)-5 b(ariables)37 b(in)h(the)i(Anderson)e(p)s(oten)m (tial)g(are)i(i.i.d.,)g Fo(H)2821 1837 y Fn(`)2892 1822 y Fp(and)f Fo(H)3154 1836 y Fn(r)3230 1822 y Fp(are)h(t)m(w)m(o)128 1969 y(indep)s(enden)m(t)32 b(random)i(Hamiltonians.)53 b(Here,)37 b(as)e(b)s(efore)f(w)m(e)h(supp)s(ose)f(that)h(Hyp)s (othesis)f(1)h(is)128 2116 y(ful\014lled.)264 2409 y(W)-8 b(e)32 b(no)m(w)e(state)i(our)e(second)g(result.)p Black 128 2619 a Fq(Theorem)42 b(2.)p Black 46 w Fc(L)-5 b(et)40 b Fo(V)924 2633 y Fm(0)1003 2619 y Fc(smal)5 b(l)40 b(enough,)h(\014x)f Fo(")e(>)f Fp(0)j Fc(and)g(let)g Fp(0)e Fo(<)f(\016)42 b Fk(\021)37 b Fo(\016)s Fp(\()p Fo(V)2832 2633 y Fm(0)2873 2619 y Fp(\))h Fo(<)f(B)30 b Fk(\000)25 b Fo(V)3302 2633 y Fm(0)3366 2619 y Fk(\000)g Fo(")p Fc(.)128 2765 y(Supp)-5 b(ose)37 b(that)g Fp(\()p Fo(H)7 b Fp(1\))38 b Fc(holds.)53 b(Then)37 b(ther)-5 b(e)37 b(exists)f Fo(\026)31 b(>)g Fp(0)p Fc(,)2213 2742 y Fp(\026)2202 2765 y Fo(L)h Fk(\025)f Fo(L)p Fp(\()p Fo(")p Fp(\))37 b Fc(such)f(that)h(if)f Fo(L)31 b(>)3306 2742 y Fp(\026)3295 2765 y Fo(L)36 b Fc(one)128 2912 y(c)-5 b(an)32 b(\014nd)h(a)f(set)704 2889 y Fp(^)694 2912 y(\012)25 b Fk(\032)g Fp(\012)32 b Fc(of)g(r)-5 b(e)g(alizations)35 b(of)d(the)h(r)-5 b(andom)34 b(p)-5 b(otential)34 b Fo(V)2573 2926 y Fn(!)2655 2912 y Fc(with)f Fl(P)2907 2926 y Fm(\003)2961 2912 y Fp(\()3006 2889 y(^)2996 2912 y(\012\))26 b Fk(\025)f Fp(1)19 b Fk(\000)f Fo(L)3434 2879 y Fi(\000)p Fn(\027)128 3059 y Fp(\()p Fo(\027)31 b Fk(\035)25 b Fp(1\))30 b Fc(such)f(that)h(for)f(al)5 b(l)29 b Fo(!)f Fk(2)1298 3036 y Fp(^)1288 3059 y(\012)h Fc(the)g(sp)-5 b(e)g(ctrum)30 b(of)f Fo(H)2087 3073 y Fn(!)2166 3059 y Fc(in)f Fp(\001)d(=)g(\()p Fo(B)17 b Fk(\000)12 b Fo(\016)n(;)j(B)i Fp(+)12 b Fo(\016)s Fp(\))30 b Fc(is)f(the)g(unions)128 3206 y(of)k(two)g(sets)g Fp(\006)649 3173 y Fi(0)649 3233 y Fn(`)714 3206 y Fc(and)h Fp(\006)957 3173 y Fi(0)957 3228 y Fn(r)994 3206 y Fc(,)f(e)-5 b(ach)33 b(dep)-5 b(ending)34 b(on)f Fo(!)i Fc(and)f Fo(L)p Fc(,)e(with)i(the)f(fol)5 b(lowing)33 b(pr)-5 b(op)g(erties:)p Black 210 3391 a(a\))p Black 49 w Fk(E)398 3358 y Fn(\013)390 3414 y(\024)473 3391 y Fk(2)25 b Fp(\006)625 3358 y Fi(0)625 3414 y Fn(\013)707 3391 y Fp(\()p Fo(\013)h Fp(=)f Fo(`;)15 b(r)s Fp(\))32 b Fc(ar)-5 b(e)34 b(a)f(smal)5 b(l)33 b(p)-5 b(erturb)g(ation)36 b(of)c Fo(E)2276 3358 y Fn(\013)2271 3414 y(\024)2352 3391 y Fk(2)24 b Fo(\033)s Fp(\()p Fo(H)2603 3405 y Fn(\013)2653 3391 y Fp(\))d Fk(\\)e Fp(\001)33 b Fc(with)1474 3615 y Fk(jE)1555 3577 y Fn(\013)1547 3637 y(\024)1625 3615 y Fk(\000)20 b Fo(E)1788 3577 y Fn(\013)1783 3637 y(\024)1838 3615 y Fk(j)25 b(\024)g Fo(e)2026 3577 y Fi(\000)p Fn(\026)2123 3521 y Fi(p)p 2183 3521 57 3 v 2183 3577 a Fn(B)2239 3521 y Fi(p)p 2298 3521 48 3 v 56 x Fn(L)2375 3615 y Fo(:)900 b Fp(\(3.15\))p Black 214 3856 a Fc(b\))p Black 49 w(F)-7 b(or)34 b Fk(E)568 3823 y Fn(\013)560 3879 y(\024)643 3856 y Fk(2)25 b Fp(\006)795 3823 y Fi(0)795 3879 y Fn(\013)876 3856 y Fc(the)33 b(curr)-5 b(ent)34 b Fk(J)1424 3823 y Fn(\013)1408 3879 y(\024)1506 3856 y Fc(of)f(the)g(asso)-5 b(ciate)g(d)35 b(eigenstate)e(satis\014es) 1469 4079 y Fk(jJ)1573 4042 y Fn(\013)1556 4102 y(\024)1643 4079 y Fk(\000)20 b Fo(J)1793 4042 y Fn(\013)1784 4102 y(\024)1842 4079 y Fk(j)26 b(\024)f Fo(e)2031 4042 y Fi(\000)p Fn(\026)2128 3985 y Fi(p)p 2187 3985 57 3 v 57 x Fn(B)2244 3985 y Fi(p)p 2303 3985 48 3 v 57 x Fn(L)2380 4079 y Fo(:)895 b Fp(\(3.16\))264 4321 y(The)41 b(idea)h(of)g(the)g (pro)s(ofs)f(of)h(Theorems)f(1)h(and)g(2)g(is)f(to)h(link)e(the)i (resolv)m(en)m(t)h(of)f(the)g(full)128 4467 y(Hamiltonian)28 b Fo(H)726 4481 y Fn(!)806 4467 y Fp(to)j(those)f(of)g(the)g(easier)g (Hamiltonians)e Fo(R)2294 4434 y Fm(0)2293 4495 y Fn(`)2334 4467 y Fp(\()p Fo(z)t Fp(\))i(\(resp.)41 b Fo(R)2813 4482 y Fn(`)2846 4467 y Fp(\()p Fo(z)t Fp(\)\),)31 b Fo(R)3123 4434 y Fm(0)3122 4490 y Fn(r)3162 4467 y Fp(\()p Fo(z)t Fp(\))g(\(resp.)128 4614 y Fo(R)197 4628 y Fn(r)235 4614 y Fp(\()p Fo(z)t Fp(\)\))i(and)e Fo(R)666 4629 y Fn(b)700 4614 y Fp(\()p Fo(z)t Fp(\).)46 b(This)30 b(is)h(ac)m(hiev)m (ed)i(via)e(a)h(decoupling)e(form)m(ula)h(for)h(the)g(resolv)m(en)m(t)g ([BCD)q(],)128 4761 y([BG)q(].)46 b(Using)32 b(it)g(w)m(e)g(can)h(do)f (deterministic)e(estimates)j(on)f(the)h(norm)e(di\013erence)h(b)s(et)m (w)m(een)h(the)128 4908 y(pro)5 b(jector)32 b Fo(P)579 4922 y Fn(H)637 4930 y Fa(!)686 4908 y Fp(\(\000\),)h(asso)s(ciated)f (to)g Fo(H)1493 4922 y Fn(!)1575 4908 y Fp(in)m(to)f(the)h(disc)f(with) f(b)s(oundary)g(\000,)i(and)f(the)h(pro)5 b(jector)128 5055 y(asso)s(ciated)40 b(to)h(one)g(of)f(the)g(easier)g(Hamiltonians.) 68 b(This)39 b(is)g(done)h(for)g(suitable)e(circles)i(\000)g(in)128 5201 y(the)30 b(complex)g(plane)f(and)h(a)h(suitable)d(set)1625 5178 y(^)1615 5201 y(\012)i(of)g(realizations)g(of)g(the)g(random)g(p)s (oten)m(tial.)40 b(Using)128 5348 y(W)-8 b(egner)33 b(estimates)g(on)g Fo(H)1065 5363 y Fn(b)1131 5348 y Fp(\(resp.)47 b Fo(H)1477 5362 y Fn(\013)1526 5348 y Fp(\))32 b(w)m(e)h(con)m(trol)g(the)g (probabilit)m(y)d(of)2779 5325 y(^)2768 5348 y(\012)i(and)g(sho)m(w)h (that)g(it)128 5495 y(can)d(b)s(e)g(made)g(large.)264 5789 y(Our)i(classi\014cation)g(of)i(the)f(sp)s(ectrum)g(via)g(the)g (quan)m(tum)g(mec)m(hanical)g(curren)m(t)g(leads)g(to)h(a)128 5935 y(w)m(ell)h(de\014ned)g(notion)g(of)i Fc(extende)-5 b(d)39 b(e)-5 b(dge)38 b(states)44 b Fp(and)36 b Fc(lo)-5 b(c)g(alize)g(d)40 b(bulk)e(states)p Fp(.)59 b(The)35 b(former)h(are)p Black 1806 6184 a Fd(7)p Black eop %%Page: 8 8 8 7 bop Black Black 128 171 a Fp(those)42 b(b)s(elonging)e(to)j(\006) 989 185 y Fn(\013)1080 171 y Fp(\(resp.)76 b(\006)1445 138 y Fi(0)1445 193 y Fn(\013)1494 171 y Fp(\),)45 b(they)d(are)h (small)d(p)s(erturbations)g(of)i(the)g(eigen)m(v)-5 b(alues)128 317 y(of)35 b Fo(\033)s Fp(\()p Fo(H)409 284 y Fm(0)402 340 y Fn(\013)452 317 y Fp(\))g(\(resp.)55 b Fo(\033)s Fp(\()p Fo(H)966 331 y Fn(\013)1015 317 y Fp(\)\))36 b(and)e(ha)m(v)m(e)j(a)e(quan)m(tum)g(mec)m(hanical)g(curren)m(t)g(of)g (order)f Fk(O)s Fp(\(1\))j(with)128 464 y(resp)s(ect)e(to)i Fo(L)p Fp(.)57 b(The)35 b(latter)h(are)h(those)f(b)s(elonging)e(to)j (\006)2151 479 y Fn(b)2185 464 y Fp(,)g(and)e(ha)m(v)m(e)i(a)f (in\014nitesimal)c(curren)m(t)128 611 y(with)25 b(resp)s(ect)i(to)h Fo(L)e Fp(\(of)i(order)e Fk(O)1295 510 y Fj(\020)1349 611 y Fo(e)1391 578 y Fi(\000)p Fn(\015)t(B)s Fm(\(log)15 b Fn(L)p Fm(\))1749 555 y Fh(2)1788 510 y Fj(\021)1842 611 y Fp(\),)28 b(they)f(\\arise")h(from)e(the)h(sp)s(ectrum)f(of)h Fo(H)3366 626 y Fn(b)3400 611 y Fp(.)39 b(It)128 758 y(is)28 b(in)m(teresting)g(to)i(note)g(that)g(our)e(description)f (leads,)i(in)f(the)h(in)m(terv)-5 b(al)29 b(inside)d(the)k(\014rst)e (Landau)128 905 y(band,)j(to)i(a)f(sp)s(ectrum)f(in)g(whic)m(h)f (extended)i(edge)h(and)e(lo)s(calized)g(bulk)f(states)j(are)g(in)m (termixed)128 1051 y(and)25 b(in)f(some)i(sense)f(there)h(is)f(no)g (\\mobilit)m(y)g(edge".)40 b(On)25 b(the)g(other)h(hand)f(in)f(the)i (in)m(terv)-5 b(al)25 b(inside)128 1198 y(the)30 b(sp)s(ectral)g(gap)h (there)f(exists)g(only)g(extended)g(edge)h(states.)128 1573 y Fg(Ac)l(kno)l(wledgemen)l(ts)128 1809 y Fp(C.F.)g(is)e(grateful) h(to)h(the)g(organizers)f(of)h(the)g(conference)g(for)f(the)h(in)m (vitation)e(to)i(rep)s(ort)f(on)g(this)128 1956 y(w)m(ork.)43 b(The)31 b(w)m(ork)h(of)f(C.F.)h(w)m(as)g(supp)s(orted)d(b)m(y)j(a)g (gran)m(t)g(from)f(the)g(F)-8 b(onds)32 b(National)f(Suisse)e(de)128 2103 y(la)h(Rec)m(herc)m(he)h(Scien)m(ti\014que.)128 2477 y Fg(References)p Black 128 2714 a Fp([AM])p Black 80 w(M.)42 b(Aizenman,)j(S.)d(Molc)m(hano)m(v:)65 b(Lo)s(calization)41 b(at)i(large)f(disorder)e(and)i(at)g(extreme)409 2861 y(energies:)e(an)31 b(elemen)m(tary)f(deriv)-5 b(ation.)30 b(Comm)m(un.)f(Math.)j(Ph)m(ys.)e Fq(157)p Fp(,)h(245)h(\(1993\))p Black 128 3049 a([BCD])p Black 49 w(P)-8 b(.)24 b(Briet,)h(J.M.)e(Com)m (b)s(es,)h(P)-8 b(.)24 b(Duclos:)37 b(Sp)s(ectral)22 b(stabilit)m(y)g(under)f(tunneling.)g(Comm)m(un.)409 3196 y(Math.)31 b(Ph)m(ys.)f Fq(126)p Fp(,)i(133)f(\(1989\))p Black 128 3384 a([BCH])p Black 49 w(J.M.)i(Barbaroux,)g(J.M.)g(Com)m(b) s(es,)g(P)-8 b(.D.)34 b(Hislop:)43 b(Lo)s(calization)32 b(near)g(band)g(edges)h(for)409 3531 y(random)c(Sc)m(hr\177)-45 b(odinger)29 b(op)s(erators.)i(Helv.)f(Ph)m(ys.)h(Acta)g Fq(70)p Fp(,)h(16)f(\(1997\))p Black 128 3719 a([BG])p Black 96 w(F.)e(Ben)m(tosela,)i(V.)e(Grecc)m(hi:)40 b(Stark)28 b(W)-8 b(annier)28 b(Ladders.)g(Comm)m(un.)g(Math.)i(Ph)m(ys.)e Fq(142)p Fp(,)409 3866 y(169)j(\(1991\))p Black 128 4054 a([dBP])p Black 54 w(S.)40 b(de)h(Bi)m(\022)-43 b(evre,)45 b(J.V.)c(Pul)m(\023)-43 b(e:)62 b(Propagating)42 b(edge)f(states)h(for) f(magnetic)h(Hamiltonian.)409 4201 y(Math.)31 b(Ph)m(ys.)f(Electr.)h (J.)f Fq(5)p Fp(,)h(no.)f(3)h(\(1999\))p Black 128 4390 a([CH])p Black 97 w(J.M.)j(Com)m(b)s(es,)g(P)-8 b(.D.)35 b(Hislop:)46 b(Landau)33 b(Hamiltonians)f(with)h(random)g(p)s(oten)m (tials:)46 b(lo-)409 4536 y(calization)30 b(and)g(the)g(densit)m(y)g (of)g(states.)i(Comm)m(un.)e(Math.)h(Ph)m(ys.)f Fq(177)p Fp(,)i(603)f(\(1996\))p Black 128 4725 a([C])p Black 165 w(J.M.)g(Com)m(b)s(es:)40 b(priv)-5 b(ate)30 b(comm)m(unication)p Black 128 4913 a([DMP1])p Black 50 w(T.C.)h(Dorlas,)i(N.)f(Macris,)g (J.V.)g(Pul)m(\023)-43 b(e:)43 b(Lo)s(calisation)31 b(in)f(a)i (single-band)e(appro)m(xima-)409 5060 y(tion)c(to)i(random)f(Sc)m (hr\177)-45 b(odinger)26 b(op)s(erators)h(in)f(a)i(magnetic)g(\014eld.) e(Helv.)h(Ph)m(ys.)g(Acta)i Fq(68)p Fp(,)409 5206 y(330)i(\(1995\))p Black 128 5395 a([DMP2])p Black 50 w(T.C.)36 b(Dorlas,)i(N.)f(Macris,)g (J.V.)g(Pul)m(\023)-43 b(e:)52 b(Lo)s(calization)36 b(in)f(single)g (Landau)g(bands.)g(J.)409 5542 y(Math.)c(Ph)m(ys.)f Fq(37)p Fp(,)h(1574)h(\(1996\))p Black 128 5730 a([DMP3])p Black 50 w(T.C.)d(Dorlas,)h(N.)g(Macris,)g(J.V.)g(Pul)m(\023)-43 b(e:)40 b(The)29 b(nature)g(of)h(the)g(sp)s(ectrum)e(for)h(a)h(Landau) 409 5877 y(Hamiltonian)e(whit)i(delta)g(impurities.)d(J.)j(Stat.)i(Ph)m (ys.)e Fq(87)p Fp(,)h(847)h(\(1997\))p Black 1806 6184 a Fd(8)p Black eop %%Page: 9 9 9 8 bop Black Black Black 128 171 a Fp([DMP4])p Black 50 w(T.C.)35 b(Dorlas,)h(N.)f(Macris,)h(J.V.)g(Pul)m(\023)-43 b(e:)49 b(Characterization)35 b(of)g(the)g(sp)s(ectrum)f(of)h(the)409 317 y(Landau)40 b(Hamiltonian)f(with)g(delta)i(impurities.)d(Comm)m (un.)i(Math.)i(Ph)m(ys.)f Fq(204)p Fp(,)j(367)409 464 y(\(1999\))p Black 128 652 a([EJK])p Black 51 w(P)-8 b(.)45 b(Exner,)j(A.)e(Jo)m(y)m(e,)k(H.)c(Ko)m(v)-5 b(arik:)69 b(Magnetic)46 b(transp)s(ort)f(in)e(a)j(straigh)m(t)f(parab)s(olic)409 799 y(c)m(hannel.)30 b(J.)g(Ph)m(ys.)g(A:)h(Math.)g(Gen.)g Fq(34)p Fp(,)g(9733)h(\(2001\))p Black 128 988 a([F])p Black 172 w(C.)i(F)-8 b(errari:)49 b(Dynamique)34 b(d'une)g(particule)g (quan)m(tique)g(dans)g(un)f(c)m(hamp)i(magn)m(\023)-43 b(etique)409 1134 y(inhomog)m(\022)g(ene.)31 b(Diploma)e(w)m(ork,)i (EPFL)f(\(1999\).)p Black 128 1323 a([F)m(GW])p Black 51 w(J.)h(F)-8 b(r\177)-45 b(ohlic)m(h,)31 b(G.M.)i(Graf,)g(J.)e(W)-8 b(alc)m(her:)44 b(On)31 b(the)h(extended)g(nature)f(of)h(edge)g(states) h(of)409 1469 y(quan)m(tum)d(Hall)f(Hamiltonians.)g(Ann.)h(Henri)f(P)m (oincar)m(\023)-43 b(e)32 b Fq(1)p Fp(,)e(405)i(\(2000\))p Black 128 1658 a([FM1])p Black 50 w(C.)c(F)-8 b(errari,)28 b(N.)g(Macris:)39 b(In)m(termixture)27 b(of)g(extended)h(edge)h(and)e (lo)s(calized)f(bulk)g(energy)409 1804 y(lev)m(els)k(in)f(macroscopic)i (Hall)e(systems.)i Fc(mp-ar)-5 b(c/02-120)p Black 128 1993 a Fp([FM2])p Black 50 w(C.)32 b(F)-8 b(errari,)33 b(N.)g(Macris:)44 b(Extended)32 b(energy)g(lev)m(els)g(in)f(the)i(gap)f (for)g(macroscopic)h(Hall)409 2140 y(systems.)d(Preprin)m(t)p Black 128 2328 a([FM3])p Black 50 w(C.)j(F)-8 b(errari,)34 b(N.)g(Macris:)47 b(Lo)s(calized)32 b(energy)i(lev)m(els)f(inside)e (Landau)i(bands.)f(In)h(prepa-)409 2475 y(ration)p Black 128 2663 a([H])p Black 163 w(B.I.)j(Halp)s(erin:)49 b(Quan)m(tized)35 b(Hall)f(conductance,)k(curren)m(t-carrying)d(edge)i(states,)h(and)409 2810 y(the)21 b(existence)h(of)f(extended)h(states)g(in)e(a)i(t)m(w)m (o-dimensional)e(disordered)f(p)s(oten)m(tial.)i(Ph)m(ys.)409 2956 y(Rev.)31 b(B)f Fq(25)p Fp(,)h(2185)i(\(1982\))p Black 128 3145 a([MMP])p Black 49 w(N.)27 b(Macris,)g(P)-8 b(.A.)28 b(Martin)d(and)h(J.V.)h(Pul)m(\023)-43 b(e:)38 b(On)26 b(Edge)g(States)h(In)f(Semi-In\014nite)e(Quan-)409 3292 y(tum)30 b(Hall)f(Systems.)h(J.)h(Ph)m(ys.)f(A:)h(Math.)g(Gen.)g Fq(32)p Fp(,)g(1985)h(\(1999\))p Black 128 3480 a([PG])p Black 98 w(R.E.)d(Prange)h(and)e(S.M.)i(Girvin:)38 b Fc(The)32 b(Quantum)g(Hal)5 b(l)31 b(E\013e)-5 b(ct)p Fp(.)30 b(New)f(Y)-8 b(ork:)41 b(Graduate)409 3627 y(T)-8 b(exts)31 b(in)e(Con)m(temp)s(orary)h(Ph)m(ysics,)g(Springer,)e(1987)p Black 128 3815 a([W])p Black 138 w(W.M.)35 b(W)-8 b(ang:)48 b(Microlo)s(calization,)34 b(p)s(ercolation)f(and)g(Anderson)g(lo)s (calization)g(for)g(the)409 3962 y(magnetic)24 b(Sc)m(hr\177)-45 b(odinger)22 b(op)s(erator)j(with)d(a)i(random)f(p)s(oten)m(tial.)h(J.) f(of)h(F)-8 b(unct.)25 b(Anal.)e Fq(146)p Fp(,)409 4108 y(1)31 b(\(1997\))p Black 1806 6184 a Fd(9)p Black eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF ---------------0203140610700--