Werner Kirsch, Ivan Veselić: Lifschitz tails for a class of Schrödinger operators with random breather-type potential

Author(s):

Werner Kirsch
Ivan Veselić

Title:

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

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 10, 2010

Mathematics Subject Classification:

35J10	[ ]
82B44	[]

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.

Keywords:

random Schrödinger operators, integrated density of states, Lifshitz tails, breather model, non-linear randomness

Language:

English

Publication time:

06/2010