Resonances and multi-particle localization at low energy

Abstract

We use a new eigenvalue concentration bound for the fluctuation of the sample mean of the random extternal potential in the multi-particle Anderson model and prove the spectral exponential and the strong dynamical localization. The results just need some weaker condition on the distribution function of the sample including a large class of probability distribution such as log-H\"older continuous or Lipshitz continuous. The method also apply to i.i.d. random Gaussian potential with independent fluctuations.