Multi-particle localization for weakly interacting Anderson tight-binding models

Abstract

We establish the complete spectral exponential and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particle system. In other words, we show the stability of the one-dimensional localization from the single-particle to multi-particle systems with an arbitrarily large but finite number of particles and for sufficient weakly interacting models. The proof uses the multi-scale analysis estimates for multi-particle systems. The common probability distribution function of the random external potential in the Anderson model is assumed to be log-Hölder continuous, so the results apply to a large class of Anderson models.