Dynamic conductivity of a two-dimensional Josephson junction array

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Abstract
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 TKT, 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=Tw>TKT. In the limit of mod T-TKT mod /TKT<0/ omega ))-1<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.