Wegner-type bounds for a two-particle Anderson model in a continuous space

TL;DR

This paper establishes Wegner-type bounds for a two-particle continuous-space Anderson model, providing probabilistic estimates for spectral intersections, which are crucial for understanding localization phenomena in disordered quantum systems.

Contribution

It extends Wegner estimates to a two-particle continuous-space Anderson model, a significant step beyond previous lattice-based results.

Findings

Derived Wegner-type bounds for the two-particle continuous Anderson model.

Provided probabilistic estimates for spectral intersections in finite volumes.

Enhanced understanding of spectral properties in multi-particle disordered quantum systems.

Abstract

We analyse a two-particle quantum system in $\R^d$ with interaction and in presence of a random external potential field with a continuous argument (an Anderson model in a continuous space). Our aim is to establish the so-called Wegner-type estimates for such a model, assessing the probability that random spectra of Hamiltonians in finite volumes intersect with a given set. For the lattice version of the two-particle model, a similar result was obtained in [8]