From fixed-energy MSA to dynamical localization: A continuing quest for elementary proofs
Mathematical Physics
2012-05-28 v1 math.MP
Abstract
We review several techniques and ideas initiated by a remarkable work by Spencer [26], used and further developed in numerous subsequent researches. We also describe a relatively short and elementary derivation of the spectral and strong dynamical Anderson localization from the fixed-energy analysis of the Green functions, obtained either by the Multi-Scale Analysis (MSA) or by the Fractional-Moment Method (FMM). This derivation goes in the same direction as the Simon--Wolf criterion [28], but provides quantitative estimates, applies also to multi-particle models and, combined with a simplified variant of the Germinet--Klein argument [20], results in an elementary proof of dynamical localization.
Cite
@article{arxiv.1205.5763,
title = {From fixed-energy MSA to dynamical localization: A continuing quest for elementary proofs},
author = {Victor Chulaevsky},
journal= {arXiv preprint arXiv:1205.5763},
year = {2012}
}