Dynamical glass in weakly nonintegrable Klein-Gordon chains
Files
Published version
Date
2019-09
Authors
Danieli, Carlo
Mithun, Thudiyangal
Kati, Yagmur
Campbell, David K.
Flach, Sergej
Version
Published version
OA Version
Citation
Carlo Danieli, Thudiyangal Mithun, Yagmur Kati, David K Campbell, Sergej Flach. 2019. "Dynamical glass in weakly nonintegrable Klein-Gordon chains.." Phys Rev E, Volume 100, Issue 3-1, pp. 032217. https://doi.org/10.1103/PhysRevE.100.032217
Abstract
Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a nonintegrable perturbation creates a coupling network in action space which can be short or long ranged. We analyze the dynamics of observables which become the conserved actions in the integrable limit. We compute distributions of their finite time averages and obtain the ergodization time scale T_{E} on which these distributions converge to δ distributions. We relate T_{E} to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations σ_{τ}^{+} dominating the means μ_{τ}^{+} and establish that T_{E}∼(σ_{τ}^{+})^{2}/μ_{τ}^{+}. The Lyapunov time T_{Λ} (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 T_{Λ}≈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 dynamical glass, where T_{E} grows dramatically by many orders of magnitude and greatly exceeds the Lyapunov time, which satisfies T_{Λ}≲μ_{τ}^{+}. This effect arises from the formation of highly fragmented inhomogeneous distributions of chaotic groups of actions, separated by growing volumes of nonchaotic regions. These structures persist up to the ergodization time T_{E}.
Description
License
"©2019 American Physical Society. The final published version of this article appears in OpenBU by permission of the publisher."