Erdos L.
Lifschitz tail in a magnetic field: the nonclassical regime
(829K, .ps file)

ABSTRACT.  We estimate the Lifschitz tail of the two dimensional
magnetic Schr\"odinger operator with a uniform magnetic 
field and random Poissonian impurities. The single site 
potential is compactly supported. We obtain the exact 
low energy asymptotics in the case of the hard-core potential 
at high density, and we prove lower and upper bounds for 
soft potential. Our methods involve magnetic localization 
techniques (both in space and energy) in addition to a modified 
version of the "enlargement of obstacles" method developed 
by A.-S. Sznitman.