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Dynamical glass in weakly nonintegrable Klein-Gordon chains.

Carlo Danieli¹, Thudiyangal Mithun¹, Yagmur Kati^1,2

¹Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon 34126, Republic of Korea.

Physical Review. E

|October 24, 2019

Summary

This summary is machine-generated.

Integrable systems perturbed by nonintegrable interactions exhibit ergodization dynamics. The ergodization time (T_{E}) depends on observable fluctuation statistics, with short-range couplings leading to dynamical glass behavior and long-range couplings showing rapid chaos diffusion.

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Area of Science:

Physics
Statistical Mechanics
Complex Systems

Background:

Integrable many-body systems possess conserved actions.
Nonintegrable perturbations introduce coupling networks in action space.

Purpose of the Study:

Analyze dynamics of observables near the integrable limit.
Determine ergodization time (T_{E}) and its relation to chaos.
Compare ergodization time with Lyapunov time (T_{Λ}).

Main Methods:

Compute finite-time average distributions of observables.
Relate T_{E} to fluctuation time statistics (mean μ_{τ}^{+} and standard deviation σ_{τ}^{+}).
Utilize a Klein-Gordon chain to model short- and long-range coupling networks.

Main Results:

Established T_{E}∼(σ_{τ}^{+})^{2}/μ_{τ}^{+} for observable fluctuations.
For long-range couplings, T_{Λ}≈σ_{τ}^{+}, indicating Lyapunov time governs ergodization.
For short-range couplings, observed dynamical glass with T_{E} >> T_{Λ}, due to fragmented chaotic regions.

Conclusions:

Ergodization time is dictated by coupling range and network structure.
Short-range couplings can lead to slow ergodization and dynamical glass states.
Lyapunov time is a key indicator for ergodization in long-range coupled systems.