Constructive Fractional-Moment Criteria for Localization in Random Operators
Mathematical Physics
2009-10-31 v1 Condensed Matter
math.MP
Probability
Spectral Theory
Abstract
We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.
Keywords
Cite
@article{arxiv.math-ph/0001035,
title = {Constructive Fractional-Moment Criteria for Localization in Random Operators},
author = {M. Aizenman and J. H. Schenker and R. M. Friedrich and D. Hundertmark},
journal= {arXiv preprint arXiv:math-ph/0001035},
year = {2009}
}
Comments
Announcement and summary of results whose proofs are given elsewhere. LaTex (10 pages), uses Elsevier "elsart" files (attached)