Thermalization of Weakly Nonintegrable FPUT and Toda Dynamics: A Lyapunov Spectrum Perspective

TL;DR

This paper investigates how weakly nonintegrable FPUT and Toda chains approach integrability by analyzing Lyapunov spectra, revealing a regime characterized by a Long Range Network of perturbations affecting thermalization.

Contribution

It provides a detailed Lyapunov spectrum analysis of FPUT and Toda chains near integrable limits, highlighting the role of long-range nonintegrable perturbations in thermalization slowdown.

Findings

Lyapunov exponents decrease near integrable limits

Rescaled Lyapunov spectra show universal scaling behavior

Evidence of Long Range Network of perturbations in dynamics

Abstract

We study the thermalization slowing down of Fermi-Past-Ulam-Tsingou (FPUT) chains and of Toda chains with nonintegrable boundaries. We focus on the transition from FPUT to harmonic chains, from FPUT to Toda chains with fixed boundaries, and from nonintegrable open boundary Toda to integrable fixed boundary Toda. We compute the Lyapunov spectrum and analyze its scaling properties upon approaching integrable limits. We analyze the scaling of the largest Laypunov exponent, the rescaled Lyapunov spectrum, and the Kolmogorov-Sinai entropy. Using additional analytic arguments we demonstrate evidence that all three cases are operating in the regime of a Long Range Network of nonintegrable perturbations.