Wegner-type bounds for a two-particle continuous Anderson model with an alloy-type external potential

TL;DR

This paper derives Wegner-type bounds for a two-particle continuous Anderson model with interactions and alloy-type external potential, providing probabilistic estimates for spectral intersections in finite volumes.

Contribution

The work introduces Wegner-type inequalities for a two-particle continuous Anderson model with alloy-type potential, advancing spectral analysis in multi-particle disordered systems.

Findings

Established probabilistic bounds for spectral intersections in finite volumes.

Extended Wegner estimates to two-particle continuous models with interactions.

Provided tools for analyzing spectral properties in multi-particle Anderson localization.

Abstract

We consider a two-particle quantum systems in a d-dimensional Euclidean space with interaction and in presence of a random external potential (a continuous two-particle Anderson model). We establish Wegner-type estimates (inequalities) for such models, assessing the probability that random spectra of Hamiltonians in finite volumes intersect a given set.