Critical current of a Josephson junction with spatial fluctuations of the order parameter

The magnetic field dependence of the critical current of a Josephson junction near the critical temperature is studied. It is proven that as the temperature approaches ${\mathit{T}}_{\mathit{c}}$, the ${\mathit{I}}_{\mathit{c}}$(H) dependence of a comparatively small Josephson junction shows random current oscillations with amplitudes of the order of those of the current itself. This mesoscopic behavior is investigated above and below the critical temperature. At temperatures above ${\mathit{T}}_{\mathit{c}}$, the supercurrent flowing in small junctions is predicted. Below ${\mathit{T}}_{\mathit{c}}$ the deviations from the periodic ‘‘Fraunhofer’’ dependence of the critical current are obtained. The correlation functions of currents are calculated for various values of the magnetic field.