Fluctuation conductivity in insulator-superconductor transitions with dissipation

We analyze here the fluctuation conductivity in the vicinity of the critical point in a 2D Josephson junction array shunted by an Ohmic resistor. We find that, at the Gaussian level, the conductivity acquires a logarithmic dependence on T/m (m is the inverse correlation length) when the dissipation is sufficiently small. In the renormalized classical regime, this logarithmic dependence gives rise to a leveling off of the resistivity at low to intermediate temperatures when fluctuations are included. We show, however, that this trend does not persist to T = 0 at which point the resistivity vanishes. The possible relationship of the leveling of the resistivity to the low temperature transport in granular superconductors is discussed.