Dynamic conductivity of a two-dimensional Josephson junction array

The author calculates the response of an N*N Josephson junction array to an oscillatory transverse vector potential. Duality transformations, and a dynamic version of Kosterlitz real space scaling, are used with the resistivity shunted junction model as a starting point. The long-wavelength low-frequency conductivity sigma (q to 0, omega , T) identical to sigma 1 +i sigma 2 is calculated, for T near T KT , the Kosterlitz-Thouless transition temperature. For fixed frequency, sigma 1 ( omega ,T) peaks at, and sigma 2 ( omega ,T) falls off at, a frequency-dependent T=T w >T KT . In the limit of mod T-T KT mod /T KT <<1,(1n( Gamma 0 / omega )) -1 <<1, dispersion relations and a sum rule are approximately satisfied. The sigma 1,2 ( omega ,T) behaviour is similar to the (phenomenological) response function of helium films to an oscillating substrate, with the difference that the quantum phase relaxation rate Gamma 0 is not a fitted parameter, but is related to the isolated-junction resistance.