97-621 Erdos L.

Lifschitz tail in a magnetic field: the nonclassical regime (improved version) (879K, .ps file) Dec 10, 97

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

Abstract. We obtain the Lifschitz tail, i.e. the exact low energy asymptotics of the integrated density of states (IDS) of the two dimensional magnetic Schr\"odinger operator with a uniform magnetic field and random Poissonian impurities. The single site potential is repulsive and it has a finite but nonzero range. We show that the IDS is a continuous function of the energy at the bottom of the spectrum. This result complements the earlier (nonrigorous) calculations by Br\'ezin, Gross and Itzykson which predict that the IDS is discontinuous at the bottom of the spectrum for zero range (Dirac delta) impurities at low density. We also elucidate the reason behind this apparent controversy. 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. This work is an improved version of the earlier paper under the same title (number 97-385).

Files: 97-621.ps