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Lifshitz Tails in Constant Magnetic Fields

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Abstract

We consider the 2D Landau Hamiltonian H perturbed by a random alloy-type potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of the corresponding integrated density of states (IDS) near the edges in the spectrum of H. If a given edge coincides with a Landau level, we obtain different asymptotic formulae for power-like, exponential sub-Gaussian, and super-Gaussian decay of the one-site potential. If the edge is away from the Landau levels, we impose a rational-flux assumption on the magnetic field, consider compactly supported one-site potentials, and formulate a theorem which is analogous to a result obtained by the first author and T. Wolff in [25] for the case of a vanishing magnetic field.

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Authors and Affiliations

  1. Département de mathématiques, Université de Paris Nord et Institut Universitaire de France, Avenue J. Baptiste Clément, 93430, Villetaneuse, France

    Frédéric Klopp

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago, Chile

    Georgi Raikov

Authors
  1. Frédéric Klopp
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  2. Georgi Raikov
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Correspondence to Frédéric Klopp.

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Communicated by B. Simon

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Klopp, F., Raikov, G. Lifshitz Tails in Constant Magnetic Fields. Commun. Math. Phys. 267, 669–701 (2006). https://doi.org/10.1007/s00220-006-0059-4

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  • DOI: https://doi.org/10.1007/s00220-006-0059-4

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