N-Body Localization for the Anderson Model with Strongly Mixing Correlated Random Potentials

Abstract

This work establishes the exponential spectral localization 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 in an energy interval near the lower edge of the spectrum of the multi-particle random 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 of the random external stochastic processes to obey the uniform log-Holder continuity condition.