Multi-particle localization for weakly interacting Anderson tight-binding models
Abstract
We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show stability of the one-dimensional localization from the single-particle to multi-particle systems with an arbitrary large but finite number of particles and for sufficient weakly interacting models. The proof uses the multi-scale analysis estimates for multi-particle systems. The common probability distribution function of the random external potential in the Anderson model is assumed to be log-H\"older continuous, so the results apply to a large class of Anderson models.
Cite
@article{arxiv.1312.4180,
title = {Multi-particle localization for weakly interacting Anderson tight-binding models},
author = {Trésor Ekanga},
journal= {arXiv preprint arXiv:1312.4180},
year = {2017}
}
Comments
19 pages minor corrections and improvements. arXiv admin note: text overlap with arXiv:1201.2339