Fluctuation phenomena below the superconducting transition

The fluctuation propagator for the superconducting order parameter belowT _c is derived for a gapless superconductor. The fluctuation of the order parameter consists of two distinct modes: the fluctuations of the phase and the modulus of the order parameter. The former fluctuation obeys a phononlike dispersion, while the latter fluctuation is described by a damping diffusion type equation. The present theory gives an account of the fluctuation-induced Josephson effect belowT _c observed recently by Carlson and Goldman.