JournalsjemsVol. 15, No. 1pp. 53–143

A comprehensive proof of localization for continuous Anderson models with singular random potentials

  • Abel Klein

    University of California, Irvine, United States
  • François Germinet

    Université de Cergy-Pontoise, France
A comprehensive proof of localization for continuous Anderson models with singular random potentials cover
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Abstract

We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution), decay of eigenfunctions correlations, and decay of the Fermi projections. We also prove log-Hölder continuity of the integrated density of states at the bottom of the spectrum.

Cite this article

Abel Klein, François Germinet, A comprehensive proof of localization for continuous Anderson models with singular random potentials. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 53–143

DOI 10.4171/JEMS/356