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

作者：Germinet Francois^*; Klein Abel

来源：Journal of the European Mathematical Society, 2013, 15(1): 53-143.

DOI：10.4171/JEMS/356

• Anderson localization
• dynamical localization
• random Schrodinger operator
• continuous Anderson model
• integrated density of states

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-Holder continuity of the integrated density of states at the bottom of the spectrum.

• 出版日期2013