Localization bounds for multiparticle systems

Michael Aizenman, Simone Warzel

Research output: Contribution to journalArticle

57 Scopus citations

Abstract

We consider the spectral and dynamical properties of quantum systems of n particles on the lattice Zd, 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.

Original languageEnglish (US)
Pages (from-to)903-934
Number of pages32
JournalCommunications In Mathematical Physics
Volume290
Issue number3
DOIs
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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