Fixed-energy multi-particle MSA implies dynamical localization
arXiv:1206.1952
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.
arXiv admin note: substantial text overlap with arXiv:1205.5763
References in corpus (8)
- A comprehensive proof of localization for continuous Anderson models with singular random potentials
- Multi-Particle Anderson Localisation: Induction on the Number of Particles
- Wegner bounds for a two-particle tight binding model
- Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
- A Wegner estimate for multi-particle random Hamiltonians
- On two-particle Anderson localization at low energies
- A remark on charge transfer processes in multi-particle systems
- Localization with Less Larmes: Simply MSA