Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34051, Korea.
Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Republic of Korea.
Phys Rev Lett. 2019 Feb 8;122(5):054102. doi: 10.1103/PhysRevLett.122.054102.
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 δ 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_{Λ}-the inverse of the largest Lyapunov exponent-reaching astonishing ratios T_{E}/T_{Λ}≥10^{8}. The microscopic reason for the observed dynamical glass is rooted 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.
经典约瑟夫森结链模型在能量密度大或约瑟夫森能量小的极限下变得可积。在这些极限附近，超导颗粒之间的约瑟夫森耦合诱导出短程不可积网络。我们计算了颗粒电荷的有限时间平均值的分布，并提取了控制它们收敛到遍历的 δ 分布的遍历时间 T_E。我们将 T_E 与电荷涨落时间的统计量联系起来，涨落时间的统计量主要由胖尾主导。与最大李雅普诺夫指数的倒数即李雅普诺夫时间 T_Λ相比，T_E 在接近可积极限时以异常快的速度增长，达到惊人的 T_E/T_Λ≥10^8 的比值。观察到的动力学玻璃的微观原因源于在较长时间内以规则的几乎可积方式演化的颗粒数量的增加，这是由于与最近邻发生共振相互作用的概率较低。我们推测，观察到的动力学玻璃是约瑟夫森结网络的一种普遍特性，与它们的空间维度无关。
