Efficient Anderson localization bounds for large multi-particle systems
Mathematical Physics
2014-04-16 v1 math.MP
Abstract
We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the whole of Z^N. Such bounds are proved here by means of a comprehensive fixed-energy multi-particle multi-scale analysis. Another feature of the paper is that we consider -- for the first time in the literature -- an infinite-range (although fast-decaying) interaction between particles. For the models under consideration we establish (1) exponential spectral localization, and (2) strong dynamical localization with sub-exponential rate of decay of the eigenfunction correlators.
Cite
@article{arxiv.1404.3978,
title = {Efficient Anderson localization bounds for large multi-particle systems},
author = {Victor Chulaevsky and Yuri Suhov},
journal= {arXiv preprint arXiv:1404.3978},
year = {2014}
}