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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Thermalization dynamics of macroscopic weakly nonintegrable maps.

Merab Malishava¹, Sergej Flach¹

¹Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, South Korea.

Chaos (Woodbury, N.Y.)

|July 1, 2022

Summary

This study reveals two thermalization regimes in nonlinear lattice dynamics. It characterizes network coupling and ergodization times, offering insights into macroscopic thermalization.

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Area of Science:

Physics
Nonlinear Dynamics
Statistical Mechanics

Background:

Studying thermalization in nonlinear systems is crucial for understanding complex dynamics.
Weakly nonintegrable systems offer a unique window into the transition from order to chaos.
Lattice dynamics provide a fundamental model for exploring emergent phenomena.

Purpose of the Study:

To identify and characterize distinct thermalization regimes in weakly nonintegrable nonlinear unitary lattice dynamics.
To investigate the relationship between network coupling (long-range vs. short-range) and observable types.
To compare thermalization timescales with Lyapunov exponents for a comprehensive understanding.

Main Methods:

Analysis of thermalization in nonlinear unitary lattice dynamics near integrable limits.
Computation of the variance of finite-time average distributions for extended and local observables.
Complementary analysis of Lyapunov spectra and comparison with ergodization time scales.

Main Results:

Identification of two distinct thermalization regimes: one associated with linear dynamics and long-range networks, the other with disconnected lattices and short-range networks.
Extraction of the ergodization time scale (T_E) marking the onset of thermalization.
Characterization of network types through the decay of variance (σ(T)) and comparison of T_E with Lyapunov time (T_L).

Conclusions:

A complete classification of weakly nonintegrable macroscopic thermalization dynamics is established.
The study provides a detailed picture of how different network structures influence thermalization processes.
The findings bridge the gap between microscopic dynamics and macroscopic thermal behavior in complex systems.