Lifshitz tails for the multi-particle continuous Anderson model

TL;DR

This paper investigates the spectral properties of the multi-particle Anderson model in the continuum, establishing the constancy of the lower spectral edge and deriving Lifshitz tail asymptotics near this edge.

Contribution

It proves the almost sure constancy of the spectral bottom and extends Lifshitz tail results from single-particle to multi-particle continuum models.

Findings

Lower spectral edge is almost surely constant.

Lifshitz asymptotics are established near the spectral bottom.

Results hold under mild assumptions on interactions and potentials.

Abstract

We consider the multi-particle Anderson model in the continuum and show that under some mild assumptions on the inter-particle interaction and the external potential, its lower spectral edge is almost surely constant and is the same with that of the single-particle model. We then obtain the lifshitz asymptotics for the multi-particle hamiltonian in the continuum near the bottom of the spectrum.