2014/02/27 by Victor Chulaevsky, Chulaevsky, Victor
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1402.6869
arXiv admin note: substantial text overlap with arXiv:1307.7047
arxiv created 2014/02/27 · arxiv updated 2014/02/28
We present the first rigorous result on Anderson localization for interacting systems of quantum particles subject to a deterministic (e.g., almost periodic) disordered external potential. For a particular class of deterministic, fermionic, Anderson-type Hamiltonians on the lattice of an arbitrary dimension, and for a large class of underlying dynamical systems generating the external potential, we prove that the spectrum is pure point, all eigenstates are unimodal and feature a uniform exponential decay. In contrast to all prior mathematical works on multi-particle Anderson localization, we do not use the induction on the number of particles.