Effective stochastic model for chaos in the Fermi-Pasta-Ulam-Tsingou chain

TL;DR

This paper models the chaotic behavior of the Fermi-Pasta-Ulam-Tsingou chain using a stochastic approach, revealing how soliton interactions and background modes influence system stability at short timescales.

Contribution

It introduces a novel stochastic model that approximates the FPUT chain's chaos by perturbing its integrable Toda chain, focusing on soliton interactions at low energies.

Findings

Lyapunov exponent decreases with energy density

Single soliton mode explains power-law profiles

Short-time chaos modeled as random Toda perturbation

Abstract

Understanding the interplay between different wave excitations, such as phonons and localized solitons, is crucial for developing coarse-grained descriptions of many-body, near-integrable systems. We treat the Fermi-Pasta-Ulam-Tsingou (FPUT) non-linear chain and show numerically that at short timescales, relevant to the largest Lyapunov exponent, it can be modeled as a random perturbation of its integrable approximation -- the Toda chain. At low energies, the separation between two trajectories that start at close proximity is dictated by the interaction between few soliton modes and an intrinsic, apparent bath representing a background of many radiative modes. It is sufficient to consider only one randomly perturbed Toda soliton-like mode to explain the power-law profiles reported in previous works, describing how the Lyapunov exponent of large FPUT chains decreases with the energy density of the system.