Conductivity and the current-current correlation measure

Jean Michel Combes; Francois Germinet; Peter D. Hislop

doi:10.1088/1751-8113/43/47/474010

Conductivity and the current-current correlation measure

Jean Michel Combes, Francois Germinet, Peter D. Hislop

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 Schrödinger 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.

Original language	English
Article number	474010
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	43
Issue number	47
DOIs	https://doi.org/10.1088/1751-8113/43/47/474010
State	Published - Nov 26 2010

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8113/43/47/474010

Cite this

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title = "Conductivity and the current-current correlation measure",

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{\"o}dinger 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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AU - Germinet, Francois

AU - Hislop, Peter D.

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N2 - 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 Schrödinger 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.

AB - 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 Schrödinger 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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DO - 10.1088/1751-8113/43/47/474010

M3 - Article

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JO - Journal of Physics A: Mathematical and Theoretical

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Conductivity and the current-current correlation measure

Abstract

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