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Lifshitz Tails in Constant Magnetic Fields

  • Frédéric KloppEmail author
  • Georgi Raikov
Article

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.

Keywords

Landau Level Random Potential Spectral Shift Function Minimax Principle Magnetic Periodicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Département de mathématiquesUniversité de Paris Nord et Institut Universitaire de FranceVilletaneuseFrance
  2. 2.Departamento de Matemáticas, Facultad de CienciasUniversidad de ChileSantiagoChile

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