97-385 Erdos L.

Lifschitz tail in a magnetic field: the nonclassical regime (829K, .ps file) Jul 1, 97

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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.

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