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Lifshitz tails for 2-dimensional random Schrödinger operators

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Abstract

The purpose of this paper is to prove that for a 2-dimensional continuous Anderson model, at an open band edge, the density of states exhibits a Lifshitz behavior. The Lifshitz exponent need not bed/2 = 1 but is determined by the behaviour of the Floquet eigenvalues of a well chosen background periodic Schrödinger operator.

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Authors and Affiliations

  1. Département de Mathématiques Institut Gaulée U.M.R. 7539 C.N.R.S, Université de Paris-Nord, 99 Avenue J.-B Clément, F-93430, Villetaneuse, France

    Frédéric Klopp

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  1. Frédéric Klopp
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  2. Thomas Wolff
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Additional information

F. K. acknowledges support form Caltech where this work was initiated, as well as from U.C.L.A and from U.C. Berkeley where it was partially done. F. K. also wants to thanks C. Sabbah for illuminating discussions on analytic vector bundles.

Thanks are due to the NSF for their support under grant DMS-0105158.

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Klopp, F., Wolff, T. Lifshitz tails for 2-dimensional random Schrödinger operators. J. Anal. Math. 88, 63–147 (2002). https://doi.org/10.1007/BF02786575

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  • DOI: https://doi.org/10.1007/BF02786575

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