Efficient Anderson localization bounds for large multi-particle systems

2014/04/15 by Victor Chulaevsky, Chulaevsky, Victor, Yuri Suhov +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1404.3978

openalex publication_date 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the whole of Z^N. Such bounds are proved here by means of a comprehensive fixed-energy multi-particle multi-scale analysis. Another feature of the paper is that we consider -- for the first time in the literature -- an infinite-range (although fast-decaying) interaction between particles. For the models under consideration we establish (1) exponential spectral localization, and (2) strong dynamical localization with sub-exponential rate of decay of the eigenfunction correlators.

Citations

• On localization in the continuous Anderson-Bernoulli model in higher dimension

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