2018/11/30 by Carlo Danieli, Thudiyangal Mithun, Yagmur Kati +2 · 1 citation
Physics and Astronomy · #nlin.CD
paper · pdf · doi:10.1103/physreve.100.032217
published as Phys. Rev. E 100, 032217 (2019)
arxiv created 2019/08/20 · arxiv updated 2019/10/02
Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a \it nonintegrable perturbation creates a coupling network in action space which can be short- or long-ranged. We analyze the dynamics of observables which turn into the conserved actions in the integrable limit. We compute distributions of their finite-time averages and obtain the ergodization time scale TE on which these distributions converge to δ-distributions. We relate TE ∼ (στ+)2/μτ+ to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations στ+ dominating the means μτ+. The Lyapunov time TΛ (the inverse of the largest Lyapunov exponent) is then compared to the above time scales. We use a simple Klein-Gordon chain to emulate long- and short-range coupling networks by tuning its energy density. For long-range coupling networks TΛ≈ στ+, which indicates that the Lyapunov time sets the ergodization time, with chaos quickly diffusing through the coupling network. For short-range coupling networks we observe a \it dynamical glass, where TE grows dramatically by many orders of magnitude and greatly exceeds the Lyapunov time, which TΛ \lesssim μτ+. This is due to the formation of a highly fragmented inhomogeneous distributions of chaotic groups of actions, separated by growing volumes of non-chaotic regions. These structures persist up to the ergodization time TE.