To the methodology of low temperature technologies: mathematical analysis of Langevin forces in superconductor

TL;DR

This paper analyzes Langevin forces within the Ginzburg-Landau framework, deriving analytical expressions and exploring their properties and asymptotic behavior in the context of superconductor fluctuations above the critical temperature.

Contribution

It introduces a novel analytical expression linking Langevin forces to the fluctuation Cooper pair wave function in superconductors.

Findings

Langevin forces are complex in nature.

Derived explicit formulas for Langevin forces.

Performed asymptotic analysis of the forces.

Abstract

Langevin forces are investigated in the framework of the phenomenological Ginzburg-Landau (GL) theory. These stochastic forces introducted in the time-dependent Ginzburg-Landau (TDGL) equation describing the superconductor transport properties above the critical temperature model the fluctuations action. We assume that there exists a profound connection between the fluctuation Cooper pair energy spectrum and the Langevin forces possible values spectrum. In investigation carried out on the basis of that hypothesis we obtain the analytical expression for Langevin forces defining them by means of order parameter, i.e., by means of the fluctuation Cooper pair wave function. Langevin forces properties are analyzed. The conlusion about their complex nature is done. Asymptotic analysis of Langevin forces is performed.