Dynamical Glass and Ergodization Times in Classical Josephson Junction Chains

Abstract

Models of classical Josephson junction chains turn integrable in the limit of large energy densities or small Josephson energies. Close to these limits the Josephson coupling between the superconducting grains induces a short range nonintegrable network. We compute distributions of finite time averages of grain charges and extract the ergodization time $T_E$ which controls their convergence to ergodic $\delta$-distributions. We relate $T_E$ to the statistics of fluctuation times of the charges, which are dominated by fat tails. $T_E$ is growing anomalously fast upon approaching the integrable limit, as compared to the Lyapunov time $T_{\Lambda}$ - the inverse of the largest Lyapunov exponent - reaching astonishing ratios $T_E/T_{\Lambda} \geq 10^8$. The microscopic reason for the observed dynamical glass is routed in a growing number of grains evolving over long times in a regular almost integrable fashion due to the low probability of resonant interactions with the nearest neighbors. We conjecture that the observed dynamical glass is a generic property of Josephson junction networks irrespective of their space dimensionality.