This article is cited in 1 paper

Localization in multiparticle Anderson models with weak interaction

T. Ekanga

Université Paris VII – Denis Diderot, Paris, France

Abstract: We prove that spectral and strong dynamical localization occurs in the one-dimensional multiparticle Anderson model with weak interaction in the continuous configuration space. To obtain these results, the interaction amplitude must be sufficiently small. The general strategy relies on an estimate in the framework of multiscale analysis. In fact, we prove that the multiscale analysis estimates for the single-particle model are unchanged in passing to multiparticle systems if the interparticle interaction is sufficiently small. The only condition imposed on the probability distribution of the external potential, which is a random field of independent identically distributed random quantities, is that it must be logarithmically continuous in the Hölder sense.

Keywords: multiparticle system, localization, weak interaction, continuity.

MSC: Primary 47B80, 47A75; Secondary 35P10

Received: 15.10.2020
Revised: 15.10.2020

DOI: 10.4213/tmf9998

 English version: Theoretical and Mathematical Physics, 2021, 206:3, 357–382

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