A comprehensive proof of localization for continuous Anderson models with singular random potentials
Abel KleinUniversity of California, Irvine, United States
François GerminetUniversité de Cergy-Pontoise, France
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. 53–143DOI 10.4171/JEMS/356