2012/06/09 by Victor Chulaevsky, Chulaevsky, Victor
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1206.1952
arXiv admin note: substantial text overlap with arXiv:1205.5763
arxiv created 2012/06/09 · arxiv updated 2012/06/12
This work is a continuation of \citeC12b 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 \citeC12b 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 \citeC08a, based on a multi-particle adaptation of techniques from Spencer's paper \citeSp88. Combined with a simplified variant of the Germinet--Klein argument \citeGK01 described in \citeC12a, 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.