N-body localization for the Anderson model with strongly mixing correlated random potentials

TL;DR

This paper proves Anderson localization for a multi-particle model with correlated, strongly mixing random potentials, demonstrating exponential decay of eigenfunctions and dynamical localization near the spectrum's lower edge.

Contribution

It establishes localization results for correlated random potentials in multi-particle systems, extending previous work to strongly mixing correlations.

Findings

Exponential decay of eigenfunctions in max-norm

Dynamical localization in Hilbert-Schmidt norm

Localization near the spectrum's lower edge

Abstract

This work establishes the Anderson localization in both the spectral exponential and the strong dynamical localization for the multi-particle Anderson tight-binding model with correlated but strongly mixing random external potential. The results are obtained near the lower edge of the spectrum of the multi-particle Hamiltonian. In particular, the exponential decay of the eigenfunctions is proved in the max-norm and the dynamical localization in the Hilbert-Schmidt norm. The proofs need the conditional probability distribution function of the random external stochastic processes to obey the uniform log-H\"older continuity condition.