Exponential decay of eigenfunctions in a continuous multi-particle Anderson model with sub-exponentially decaying interaction

TL;DR

This paper proves that in a multi-particle Anderson model with sub-exponentially decaying interaction, eigenfunctions at low energies decay exponentially, strengthening previous results that only established sub-exponential decay.

Contribution

It demonstrates exponential decay of eigenfunctions in a multi-particle Anderson model with sub-exponentially decaying interaction, improving prior sub-exponential decay results.

Findings

Eigenfunctions decay exponentially at low energies.

Strengthens previous sub-exponential decay results.

Supports strong dynamical localization in the model.

Abstract

This short note is a complement to our recent paper [2] where we established strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. We show that the localized eigenfunctions at low energies actually decay exponentially fast. This improves the results by Fauser and Warzel who established sub-exponential decay of eigenfunctions in presence of a sub-exponentially decaying interaction.