Conductivity and the current-current correlation measure
Mathematical Physics
2015-05-19 v1 Functional Analysis
math.MP
Abstract
We review various formulations of conductivity for one-particle Hamiltonians and relate them to the current-current correlation measure. We prove that the current-current correlation measure for random Schr\"odinger operators has a density at coincident energies provided the energy lies in a localization regime. The density vanishes at such energies and an upper bound on the rate of vanishing is computed. We also relate the current-current correlation measure to the localization length.
Cite
@article{arxiv.1008.5344,
title = {Conductivity and the current-current correlation measure},
author = {J. M. Combes and F. Germinet and P. D. Hislop},
journal= {arXiv preprint arXiv:1008.5344},
year = {2015}
}