 02389 Francois Germinet, Abel Klein
 The Anderson metalinsulator transport transition
(370K, .ps)
Sep 19, 02

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We discuss a new approach to the metalinsulator
transition for random operators, based on transport instead of
spectral properties. It applies to random Schr\"odinger operators,
acoustic operators in random media, and Maxwell operators in
random media. We define a
local transport exponent $\beta(E)$, and set the \emph{metallic
transport region} to be the part of the spectrum with nontrivial
transport (i.e., $\beta(E)>0$). The \emph{strong insulator region}
is taken to be the part of the
spectrum where the random operator exhibits strong dynamical
localization in the HilbertSchmidt norm, and hence no transport.
For the standard random operators satisfying a Wegner estimate,
these metallic and insulator regions
are shown to be complementary sets in the spectrum of the random
operator, and the local transport exponent $\beta(E)$ provides a
characterization of the \emph{metalinsulator transport transition}.
If such a transition occurs, then $\beta(E)$ has to be discontinuous
at a \emph{transport mobility edge}: if the transport is nontrivial
then $\beta(E)\ge \frac 1{2bd}$, where $d$ is the space dimension and
$b\ge 1$ is the power of the volume in Wegner's estimate.
We also examine the transport transition for random
polymer models, where the random dimer models provide
explicit examples of the transport transition and of a
transport mobility edge.
 Files:
02389.src(
02389.keywords ,
trprocmparc.ps )