Wegner bounds for N-body interacting Bernoulli-Anderson models in one dimension

TL;DR

This paper establishes Wegner bounds for one-dimensional multi-particle Bernoulli-Anderson models with weak interactions, leading to proofs of Anderson localization in spectral and dynamical senses.

Contribution

It provides the first Wegner bounds for multi-particle models with Bernoulli distributions in one dimension under weak interactions.

Findings

Proved Wegner bounds for multi-particle Bernoulli models

Established Anderson localization in spectral and dynamical senses

Applicable to models with singular probability distributions

Abstract

Under the weak interaction regime, we prove the one and the two volumes Wegner type bounds for one dimensional multi-particle models on the lattice and for very singular probability distribution functions such as the Bernoulli measures. The results imply the Anderson loclalization in both the spectral exponential and the strong dynamical localization for the one dimensional multi-particle Bernoulli-Anderson model with weak interaction.