Conductivity due to classical phase fluctuations in a model for high-Tc superconductors

We consider the real part of the conductivity, sigma(1:alpha alpha)(omega), arising from classical phase fluctuations in high-T-c superconductors. We show that integral(0)(infinity)sigma(1:alpha alpha)d omega not equal 0 below the superconducting transition temperature T-c, provided there is some quenched disorder in the system. Furthermore, for a fixed amount of quenched disorder, this integral at low temperatures is proportional to the zero-temperature superfluid density, in agreement with experiment. We calculate sigma(1:alpha alpha)(omega) explicitly for a model of overdamped phase fluctuations.