Localization Bounds for Multiparticle Systems View Full Text


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Article Info

DATE

2009-09

AUTHORS

Michael Aizenman, Simone Warzel

ABSTRACT

We consider the spectral and dynamical properties of quantum systems of n particles on the lattice \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}^d}$$\end{document} , 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. More... »

PAGES

903-934

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-009-0792-6

DOI

http://dx.doi.org/10.1007/s00220-009-0792-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1049998851


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