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Localization Bounds for Multiparticle Systems

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Abstract

We consider the spectral and dynamical properties of quantum systems of n particles on the lattice \({\mathbb{Z}^d}\) , of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term includes a random potential with iid values at the lattice sites and a finite-range interaction. Two basic parameters of the model are the strength of the disorder and the strength of the interparticle interaction. It is established here that for all n there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed through bounds on the transition amplitudes, which are uniform in time and decay exponentially in the Hausdorff distance in the configuration space. The results are derived through the analysis of fractional moments of the n-particle Green function, and related bounds on the eigenfunction correlators.

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Author notes

  1. Simone Warzel

    Present address: Zentrum Mathematik, TU München, München, Germany

Authors and Affiliations

  1. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, USA

    Michael Aizenman & Simone Warzel

Authors
  1. Michael Aizenman
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  2. Simone Warzel
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Correspondence to Michael Aizenman.

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Communicated by B. Simon

© 2009 The Authors. Reproduction of this article for non-commercial purposes by any means is permitted.

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Aizenman, M., Warzel, S. Localization Bounds for Multiparticle Systems. Commun. Math. Phys. 290, 903–934 (2009). https://doi.org/10.1007/s00220-009-0792-6

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  • DOI: https://doi.org/10.1007/s00220-009-0792-6

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