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arXiv · 1008.5344

Conductivity and the current-current correlation measure

J. M. Combes·F. Germinet·P. D. Hislop
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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.

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J. M. Combes, F. Germinet, P. D. Hislop. 2010-08-31. Conductivity and the current-current correlation measure. https://doi.org/10.1088/1751-8113/43/47/474010

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