Multi-Scale Jacobi Method for Anderson Localization
Mathematical Physics
2016-01-11 v3 Disordered Systems and Neural Networks
math.MP
Probability
Abstract
A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837].
Keywords
Cite
@article{arxiv.1406.2957,
title = {Multi-Scale Jacobi Method for Anderson Localization},
author = {John Z. Imbrie},
journal= {arXiv preprint arXiv:1406.2957},
year = {2016}
}
Comments
34 pages, 8 figures, clarifications and corrections for published version; more detail in Section 4.5