Anderson localization for a multi-particle model with alloy-type external potential

TL;DR

This paper proves exponential localization for a multi-particle Anderson model with short-range interactions and alloy-type external potential, showing eigenfunctions decay exponentially near the spectrum's lower edge.

Contribution

It establishes exponential localization in a multi-particle setting with alloy-type potential and interactions, extending previous single-particle results.

Findings

Eigenfunctions decay exponentially near the spectrum's lower edge

Localization holds in arbitrary dimensions

Results include models with short-range interactions

Abstract

We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we prove that all eigenfunctions with eigenvalues near the lower edge of the spectrum decay exponentially.