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

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.