Physics – Mathematical Physics
Scientific paper
2011-05-01
Physics
Mathematical Physics
Results were slightly improved, misprints were corrected, etc
Scientific paper
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-H\" older continuity of the integrated density of states at the bottom of the spectrum.
Germinet François
Klein Abel
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