425 research outputs found
Dynamical glass in weakly non-integrable Klein-Gordon chains
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 on which these distributions
converge to -distributions. We relate to the statistics of fluctuation times of the
observables, which acquire fat-tailed distributions with standard deviations
dominating the means . The Lyapunov time
(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 , 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 grows dramatically by many orders of magnitude
and greatly exceeds the Lyapunov time, which .
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
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