Flux noise and Fluctuation conductivity in Unfrustrated Josephson Junction Arrays

Abstract

We study the flux noise $S_{\Phi }(\omega )$ and finite frequency conductivity ${\sigma }_1(\omega )$ in two dimensional unfrustrated Josephson junction arrays (JJA's), by numerically solving the equations of the coupled overdamped resistively-shunted-junction model with Langevin noise. We find that $S_{\Phi }(\omega )\propto {\omega }^{-3/2}$ at high frequencies $\omega$ and flattens at low $\omega$, indicative of vortex diffusion, while ${\sigma }_1\propto {\omega }^{-2}$ at sufficiently high $\omega$. Both quantities show clear evidence of critical slowing down and possibly scaling behavior near the Kosterlitz-Thouless-Berezinskii (KTB) transition. The critical slowing down of $S_{\Phi }$, but not its frequency dependence, is in agreement with recent experiments on Josephson junction arrays.

12 pages, RevTeX, eight figures in postscript

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