Dynamical glass in weakly non-integrable many-body systems
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Published version
Date
2018-11-20
DOI
Authors
Campbell, David K.
Danieli, Carlo
Kati, Yagmur
Mithun, Thudiyangal
Flach, Sergej
Version
Published version
OA Version
Citation
David Campbell, C. Danieli, Yagmur Kati, T. Mithun, S. Flach. 2018. "Dynamical glass in weakly non-integrable many-body systems." arXiv:1811.10832, https://arxiv.org/abs/1811.10832.
Abstract
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∼(σ+τ)2/μ+τ to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations σ+τ dominating the means μ+τ. 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≈σ+τ, 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≲μ+τ. 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.