Dynamical Glass Phase and Ergodization Times in Josephson Junction Chains*

Models of 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 $T_E/ T_{\Lambda} \ge 10^8$. The microscopic reason for the observed dynamical glass phase 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 phase is a generic property of Josephson junction networks irrespective of their space dimensionality.