Localization at low energies in the multi-particle tight-binding model

2012/01/11 by Trésor Ekanga, Ekanga, Trésor
Mathematics · Physics and Astronomy · #47A75. Secondary 35P10 #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 47B80 #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1201.2339

openalex publication_date 2012/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the multi-particle Anderson tight-binding model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low energy regime the multi-particle multi-scale analysis initially developed by Chulaevsky and Suhov in the high disorder limit, if the marginal probability distribution of the i.i.d. random variables is log-Hölder continuous and obtain the spectral exponential and strong dynamical localization near the bottom of the spectrum.

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