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

Funding

Funders	Funder number
National Science Foundation (NSF)
Directorate for Mathematical and Physical Sciences	0803379

ASJC Scopus subject areas

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

Access to Document

10.1088/1751-8113/43/47/474010

Cite this

@article{94e38d1b85ea42c682cc5d476b74db3f,

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.",

author = "Combes, {Jean Michel} and Francois Germinet and Hislop, {Peter D.}",

year = "2010",

month = nov,

day = "26",

doi = "10.1088/1751-8113/43/47/474010",

language = "English",

volume = "43",

number = "47",

}

TY - JOUR

T1 - Conductivity and the current-current correlation measure

AU - Combes, Jean Michel

AU - Germinet, Francois

AU - Hislop, Peter D.

PY - 2010/11/26

Y1 - 2010/11/26

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.

UR - http://www.scopus.com/inward/record.url?scp=78649653304&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649653304&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/43/47/474010

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

M3 - Article

AN - SCOPUS:78649653304

SN - 1751-8113

VL - 43

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 47

M1 - 474010

ER -

Conductivity and the current-current correlation measure

Abstract

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this