## Vortex Noise and Fluctuation Conductivity in Josephson
Junction Arrays

#### Ing-Jye Hwang and D. Stroud, Department of Physics,
The Ohio State University, Columbus, Ohio 43210

We study the vortex number noise S_v(omega) and fluctuation conductivity
sigma_1(omega) in two-dimensional Josephson
junction arrays (JJA's) at three different applied magnetic fields,
corresponding to zero, one-half and 1/24 of a flux quantum per plaquette
(f = 0, 1/2, and 1/24). S_v and sigma_1 are obtained
by numerically solving the equations for the coupled overdamped
resistively-shunted-junction model with Langevin noise to simulate the effects
of temperature. In all three cases, we find that
S_v(omega) is proportional to omega^(-3/2) at high frequencies omega and
flattens out to become frequency-independent at low omega,
indicative of vortex diffusion, while sigma_1 is proportional to omega^(-2)
at sufficiently high omega and to omega^0 at low frequencies.
Both quantities show clear evidence of
critical slowing down and a simplified scaling behavior near the
normal-to-superconducting transitions at f = 0 and f = 1/2, indicating that
the vortex diffusion coefficient is approaching zero and the charge carrier
relaxation time is diverging at these temperatures. At f = 1/24, there is
no clear phase transition; instead, the vortex diffusion coefficient diminishes
continuously as the temperature is lowered towards zero.
The critical slowing down of S_v(omega), but not its frequency dependence,
is in agreement with recent experiments on the flux noise S_Phi(omega)
in Josephson junction arrays, which show a 1/omega frequency dependence.
We speculate about some possible reasons for the absence of a 1/omega
frequency regime.
PACS numbers: 74.50.+r, 74.40.+k, 64.60.Fr