Wegner bounds for a two-particle tight binding model

TL;DR

This paper establishes Wegner-type estimates for a two-particle quantum lattice model with interaction and random external potential, using Stollmann's lemma, to analyze spectral properties.

Contribution

It introduces Wegner bounds for a two-particle lattice system with interaction, extending spectral analysis tools to multi-particle disordered models.

Findings

Wegner estimates are proven for the two-particle model.

The approach utilizes Stollmann's lemma effectively.

Results contribute to understanding spectral properties of interacting disordered systems.

Abstract

We consider a quantum two-particle system on a d-dimensional lattice with interaction and in presence of an IID external potential. We establish Wegner-typer estimates for such a model. The main tool used is Stollmann's lemma.