Flux noise and Fluctuation conductivity in Unfrustrated Josephson Junction Arrays

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.