Localization at low energies in the multi-particle tight-binding model
Abstract
We consider the multi-particle Anderson tight-binding model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low energy regime the multi-particle multi-scale analysis initially developed by Chulaevsky and Suhov in the high disorder limit, if the marginal probability distribution of the i.i.d. random variables is log-H\"older continuous and obtain the spectral exponential and strong dynamical localization near the bottom of the spectrum.
Cite
@article{arxiv.1201.2339,
title = {Localization at low energies in the multi-particle tight-binding model},
author = {Trésor Ekanga},
journal= {arXiv preprint arXiv:1201.2339},
year = {2013}
}
Comments
31 pages. Important improvements have been made in the initial text including the reformulation of the results. This version only treats the low energy regime in order to keep the paper in a reasonable length. The weak interaction regime which has also been improved is the object of a separated paper. Suffix informations have also been added