Lifshitz tails for a class of Schrödinger operators with random breather-type potential

Abstract

We derive bounds on the integrated density of states for a class of Schrödinger operators with a random potential. The potential depends on a sequence of random variables, not necessarily in a linear way. An example of such a random Schrödinger operator is the breather model, as introduced by Combes, Hislop and Mourre. For these models we show that the integrated density of states near the bottom of the spectrum behaves according to the so called Lifshitz asymptotics. This result can be used to prove Anderson localization in certain energy/disorder regimes.

References in corpus (4)

• Moment Analysis for Localization in Random Schroedinger Operators
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• Minimizing the ground state energy of an electron in a randomly deformed lattice
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• Peculiar spectral statistics of ensembles of trees and star-like graphs
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• Quantum Hamiltonians with weak random abstract perturbation. II. Localization in the expanded spectrum
• Wegner estimate for random divergence-type operators monotone in the randomness