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arXiv · 1312.4180

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

Trésor Ekanga
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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.

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Trésor Ekanga. 2013-12-15. Multi-particle localization for weakly interacting Anderson tight-binding models. https://arxiv.org/abs/1312.4180

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