Density of States under non-local interactions II. Simplified polynomially screened interactions

TL;DR

This paper investigates the regularity and localization properties of the density of states in Anderson models with polynomially decaying, non-local interactions, demonstrating infinite smoothness of the IDS and establishing Anderson localization.

Contribution

It provides a detailed analysis of polynomially screened interactions and proves infinite smoothness of the IDS along with spectral and dynamical localization results.

Findings

Infinite smoothness of the IDS in finite domains

Spectral localization in models with polynomial decay interactions

Dynamical localization confirmed for the considered models

Abstract

Following [5], 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. In the present work, we study in detail a class of polynomially decaying interaction potentials of rather artificial (piecewise-constant) form, and give a complete proof of infinite smoothness of the IDS in an arbitrarily large finite domain subject to the fluctuations of the entire, infinite random environment. A variant of this result, based as in [5] on the harmonic analysis of probability measures, results in a proof of spectral and dynamical Anderson localization in the considered models.