JournalsjstVol. 7, No. 1pp. 269–320

Efficient Anderson localization bounds for large multi-particle systems

  • Victor Chulaevsky

    Université de Reims, France
  • Yuri Suhov

    University of Cambridge, UK
Efficient Anderson localization bounds for large multi-particle systems cover
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Abstract

We study multi-particle interactive quantum disordered systems on a polynomially growing countable connected graph (Z,E\mathcal Z, \mathcal E). The main novelty is to give localization bounds uniform in finite volumes (subgraphs) in ZN\mathcal Z^N as well as for the whole of ZN\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 NN-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.

Cite this article

Victor Chulaevsky, Yuri Suhov, Efficient Anderson localization bounds for large multi-particle systems. J. Spectr. Theory 7 (2017), no. 1, pp. 269–320

DOI 10.4171/JST/163