Density of States under non-local interactions III. N-particle Bernoulli--Anderson model

TL;DR

This paper investigates the spectral properties and localization phenomena of a two-particle Anderson model with infinite-range interactions and power-law decaying potentials, establishing localization at low energies.

Contribution

It extends previous work to analyze two-particle models with non-local interactions and proves localization results for potentials with power-law decay.

Findings

Spectral localization at low energies

Exponential decay of eigenfunctions

Localization for power-law decaying potentials

Abstract

Following [7,8], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions and arbitrary nontrivial probability distributions of the site potentials. In the present work, we study $2$-particle Anderson Hamiltonians on a lattice and prove spectral and strong dynamical localization at low energies, with exponentially decaying eigenfunctions, for a class of site potentials featuring a power-law decay.