Relaxation of the Superconducting Order Parameter

The creation and annihilation of quasiparticles in a superconductor through their interaction with the phonon field is examined. At low frequencies this appears to be the main mechanism leading to relaxation of the order parameter in a superconductor. The relaxation time becomes long both close to $T_c$ and at low temperatures. Close to $T_c$, a diffusion equation for the order parameter is obtained. The correlation in time of the fluctuations of the order parameter is examined. A weak coupling between the amplitude and phase of the order parameter is shown to lead to a slow diffusion of the phase of the order parameter.