Thermal fluctuations in 1D superconducting samples

For a system that obeys diffusive evolution, an additional term due to thermal fluctuations should be added. We present an intuitive derivation of the distribution of this term. The formalism developed to deal with fluctuations can be incorporated into two models that are widely used in the dynamics of superconductors: the time-dependent Ginzburg-Landau model and the Kramer-Watts-Tobin model. We review three problems that can be studied with these models: supercurrent flow around a ring close to T-c; fluctuations of the supercurrent in a filament that bridges between two bulk superconductors with order parameters at a given phase difference; and the Kibble-Zurek mechanism, intended to describe phase transitions that are governed by kinetics rather than by thermodynamics, in the case of a superconducting loop.