Uniform decay of unimodal states and non-local Minami estimates for a class of Fermionic Anderson models with deterministic potentials

Abstract

We prove Anderson localization for a class of interactive Fermionic Hamiltonians in a deterministic (including some quasi-periodic) disordered external potential on a one-dimensional lattice. As in our earlier paper on 1-particle Hamiltonians (Chulaevsky, 2014), and in contrast to a recent work (J. Bourgai and I. Kachkovskiy, 2019), the sampling function on the phase space of the dynamical system generating the external potential is not even continuous. As a complement to the parametric analysis of the eigenpairs, we also prove some analogs of the Minami estimate for pairs of eigenvalues in arbitrarily placed intervals, not necessarily nested, or close to/distant from each other.