Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires

Jorge Berger
Phys. Rev. B 75, 184522 – Published 22 May 2007

Abstract

Many analyses based on the time-dependent Ginzburg-Landau model are not consistent with statistical mechanics, because thermal fluctuations are not taken into account correctly. We use the fluctuation-dissipation theorem in order to establish the appropriate size of the Langevin terms, and thus ensure the required consistency. Fluctuations of the electromagnetic potential are essential, even when we evaluate quantities that do not directly depend on it. Our method can be cast in gauge-invariant form. We perform numerous tests, and all the results are in agreement with statistical mechanics. We apply our method to evaluate paraconductivity of a superconducting wire. The Aslamazov-Larkin result is recovered as a limiting situation. Our method is numerically stable and the nonlinear term is easily included. We attempt a comparison between our numerical results and the available experimental data. Within an appropriate range of currents, phase slips occur, but we found no evidence for thermally activated phase slips. We studied the behavior of a moderate constriction. A constriction pins and enhances the occurrence of phase slips.

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  • Received 5 June 2006

DOI:https://doi.org/10.1103/PhysRevB.75.184522

©2007 American Physical Society

Authors & Affiliations

Jorge Berger*

  • Physics Department, Ort Braude College, P.O. Box 78, 21982 Karmiel, Israel

  • *Electronic address: jorge.berger@braude.ac.il

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Issue

Vol. 75, Iss. 18 — 1 May 2007

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