Thermalization dynamics of macroscopic weakly nonintegrable maps

TL;DR

This paper investigates how weakly nonintegrable lattice systems thermalize, identifying different regimes and timescales, and analyzing the network structure of observable couplings to classify the thermalization dynamics.

Contribution

It provides a comprehensive classification of thermalization regimes in weakly nonintegrable maps, linking network structure, timescales, and Lyapunov spectra.

Findings

Identification of two distinct thermalization regimes near integrable limits.

Derivation of ergodization time scale $T_E$ and its relation to network type.

Comparison of ergodization time with Lyapunov time $T_{ ext{Lambda}}$.

Abstract

We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity the almost conserved actions correspond to extended observables which are coupled into a long-range network. For weakly connected lattices the corresponding local observables are coupled into a short-range network. We compute the evolution of the variance $\sigma^2(T)$ of finite time average distributions for extended and local observables. We extract the ergodization time scale $T_E$ which marks the onset of thermalization, and determine the type of network through the subsequent decay of $\sigma^2(T)$. We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time $T_{\Lambda}$ with $T_E$. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.