The Ginzburg-Landau Equations for Superconductivity with Random Fluctuations

Abstract

Thermal fluctuations and material inhomogeneities have a large effect on superconducting phenomena, possibly inducing transitions to the non-superconducting state. To gain a better understanding of these effects, the Ginzburg—Landau model is studied in situations for which the described physical processes are subject to uncertainty. An adequate description of such processes is possible with the help of stochastic partial differential equations. The boundary value problem of Neumann type for the stochastic Ginzburg—Landau equations with additive and multiplicative white noise is investigated. We use white noise with minimal restriction on its independence property. The existence and uniqueness of weak and strong statistical solutions are proved. Our approach is based on using difference schemes for the Ginzburg— Landau equations.