Ginzburg-Landau equations with consistent Langevin terms for nonuniform wires

Abstract

Many analyses based on the time-dependent Ginzburg--Landau model are not consistent with statistical mechanics, because thermal fluctuations are not taken correctly into account. 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 depend directly 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.

arXiv commentcontains new sections that deal with phase slips

References in corpus (8)

• Quantum Phase Slips in Superconducting Nanowires
• Current-voltage characteristics of quasi-one-dimensional superconductors: An S-curve in the constant voltage regime
• Condition of the occurrence of phase slip centers in superconducting nanowires under applied current or voltage
• Induction of dc voltage, proportional to the persistent current, by external ac current on system of inhomogeneous superconducting loops
• Flux-Induced Vortex in Mesoscopic Superconducting Loops
• Absence of the Transition into Abrikosov Vortex State of Two-Dimensional Type-II Superconductor with Weak Pinning
• Effects of thermal fluctuations on the magnetic behavior of mesoscopic superconductors
• Instabilities and resistance fluctuations in thin accelerated superconducting rings

Cited by in corpus (7)

• Multi-Parton Scattering Amplitudes via On-Shell Methods
• Influence of Thermal Fluctuations on Uniform and Nonuniform Superconducting Rings according to the Ginzburg--Landau and the Kramer--Watts-Tobin Models
• Flux-induced Nernst effect in a superconducting loop
• Supercurrent fluctuations in short filaments
• Characterization of the spontaneous symmetry breaking due to quenching of a one-dimensional superconducting loop
• Topological thermalization via vortex formation in ultra-fast quenches
• A case of thermodynamic failure in the Ginzburg--Landau approach to fluctuation superconductivity