Multi-particle localization at low energy for the multi-dimensional continuous Anderson model

2017/02/13 by Trésor Ekanga, Ekanga, Trésor
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Chromodynamics and Particle Interactions #Random Matrices and Applications #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1702.03945

openalex publication_date 2017/02/13 · openalex created_date 2017/02/24 · openalex updated_date 2026/07/28

Abstract

We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of the spectrum are almost surely constant in absence of ergodicity. We stress that this result is not quite obvious and has to be handled carefully. In addition, we prove the spectral exponential and the strong dynamical localization of the continuous multi-particle Anderson model at low energy. The proof based on the multi-particle multi-scale analysis bounds, needs the values of the external random potential to be independent and identically distributed (i.i.d.) whose common probability distribution is at least Log-Hölder continuous.

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