On two-particle Anderson localization at low energies

TL;DR

This paper proves exponential spectral localization for a two-particle lattice Anderson model at low energies, extending previous methods to a broader class of random potentials.

Contribution

It introduces a new proof of localization at low energies using multi-scale analysis, expanding the applicability beyond high disorder and specific potential types.

Findings

Exponential spectral localization established at low energies.

Method applies to a broader class of random potentials.

Extends previous localization results to two-particle systems.

Abstract

We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale analysis developed earlier by Chulaevsky and Suhov (2009) in the case of high disorder. Our method applies to a larger class of random potentials than in Aizenman and Warzel (2009) where dynamical localization was proved with the help of the fractional moment method.