English

Multi-particle localization for weakly interacting Anderson tight-binding models

Mathematical Physics 2017-03-23 v5 math.MP Probability Spectral Theory

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.

Keywords

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

R2 v1 2026-06-22T02:27:57.868Z