Flux noise and Fluctuation conductivity in Unfrustrated Josephson Junction Arrays

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We study the flux noise SΦ(ω) and finite frequency conductivity σ₁(ω) 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 SΦ(ω)∝ ω⁻³/² at high frequencies ω and flattens at low ω, indicative of vortex diffusion, while σ₁ ∝ ω⁻² at sufficiently high ω. 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 SΦ, but not its frequency dependence, is in agreement with recent experiments on Josephson junction arrays.