95-144 Kurt Broderix, Dirk Hundertmark,, Werner Kirsch, Hajo Leschke

The Fate of Lifshits Tails in Magnetic Fields (97K, uuencoded zipped postscript) Mar 10, 95

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Abstract. We investigate the integrated density of states of the Schr\"odinger operator in the Euclidean plane with a perpendicular constant magnetic field and a random potential. For a Poisson random potential with a non-negative algebraically decaying single-impurity potential we prove that the leading asymptotic behaviour for small energies is always given by the corresponding classical result in contrast to the case of vanishing magnetic field. We also show that the integrated density of states of the operator restricted to the eigenspace of any Landau level exhibits the same behaviour. For the lowest Landau level, this is in sharp contrast to the case of a Poisson random potential with a delta-function impurity potential.

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