Wegner estimate for Landau-breather Hamiltonians

TL;DR

This paper establishes a Wegner estimate for Landau Hamiltonians with breather-type random potentials, demonstrating Hölder continuity of the integrated density of states despite the non-linear dependence on randomness.

Contribution

The paper introduces a novel approach to handle non-linear dependence in Landau Hamiltonians with breather potentials, proving a Wegner estimate under specific conditions.

Findings

Wegner estimate proven for Landau-breather Hamiltonians

Hölder continuity of the integrated density of states established

Method addresses non-linear dependence challenges

Abstract

We consider Landau Hamiltonians with a weak coupling random electric potential of breather type. Under appropriate assumptions we prove a Wegner estimate. It implies the Hoelder continuity of the integrated density of states. The main challenge is the problem how to deal with non-linear dependence on the random parameters.