Time-dependent Ginzburg-Landau theory is used to investigate the resistive transition in a "one-dimensional" superconductor as a function of temperature and current through the wire. A diagrammatic expansion, in powers of the interaction between fluctuations, is described for the electrical conductivity. The conductivity is then calculated using a Hartree-Fock approximation for the interaction. When large currents flow through the wire, an unstable region is found near the depressed critical temperature, suggesting possible hysteresis effects which may have been observed in recent experiments.

• Received 8 January 1971

DOI:https://doi.org/10.1103/PhysRevB.3.3768