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arXiv · 1206.1952

Fixed-energy multi-particle MSA implies dynamical localization

Victor Chulaevsky
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Abstract

This work is a continuation of \cite{C12b} where we described two elementary derivations of the variable-energy MSA bounds from their fixed-energy counterparts, in the framework of single-particle disordered quantum particle systems on graphs with polynomially bounded growth of balls. Here the approach of \cite{C12b} is extended to multi-particle Anderson Hamiltonians with interaction; it plays a role similar to that of the Simon--Wolf criterion for single-particle Hamiltonians. A simplified, fixed-energy multi-particle MSA scheme was developed in our earlier work \cite{C08a}, based on a multi-particle adaptation of techniques from Spencer's paper \cite{Sp88}. Combined with a simplified variant of the Germinet--Klein argument \cite{GK01} described in \cite{C12a}, the outcome of the fixed-energy analysis results in an elementary proof of multi-particle dynamical localization with the decay of eigenfunction correlators faster than any power-law.

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Victor Chulaevsky. 2012-06-09. Fixed-energy multi-particle MSA implies dynamical localization. https://arxiv.org/abs/1206.1952

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