Journal of Spectral Theory

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Volume 7, Issue 1, 2017, pp. 269–320
DOI: 10.4171/JST/163

Published online: 2017-03-22

Efficient Anderson localization bounds for large multi-particle systems

Victor Chulaevsky[1] and Yuri Suhov[2]

(1) Université de Reims, France
(2) University of Cambridge, UK

We study multi-particle interactive quantum disordered systems on a polynomially growing countable connected graph ($\mathcal Z, \mathcal E$). The main novelty is to give localization bounds uniform in finite volumes (subgraphs) in $\mathcal Z^N$ as well as for the whole of $\mathcal Z^N$. Such bounds are proved here by means of a comprehensive fixed-energy multi-particle multiscale analysis. We consider – for the first time in the literature – a discrete $N$-particle model with an infinite-range, sub-exponentially decaying interaction, and establish (1) exponential spectral localization, and (2) strong dynamical localization with sub-exponential rate of decay of the eigenfunction correlators with respect to the natural symmetrized distance in the multi-particle configuration space.

Keywords: Multi-particle Anderson localization, dynamical localization

Chulaevsky Victor, Suhov Yuri: Efficient Anderson localization bounds for large multi-particle systems. J. Spectr. Theory 7 (2017), 269-320. doi: 10.4171/JST/163