Work

Random Initial Data and Average Shock Time in the Fermi-Pasta-Ulam-Tsingou Chain

Year: 2026

Type: article

Abstract: We investigate the dynamics of the Fermi-Pasta-Ulam-Tsingou chain with long-wavelength random initial data. When the energy per particle is small, thermal equilibrium is not reached on a fast timescale, and the system enters prethermalization. The formation of the prethermal state is characterized by the development of a Burgers-type shock and the onset of a turbulentlike spectrum with a time dependent exponent ζ(t) in the inertial range. We perform a significant step forward by demonstrating that these features are robust under generic long-wavelength random initial conditions. By employing advanced probabilistic techniques inspired by the works of Dudley and Talagrand, we derive a sharp asymptotic expression for the average shock time in the thermodynamic limit. For large p, this time scales as (psqrt[logp])^{-1}, where p is the number of excited modes, proving that it is an intensive quantity up to a logarithmic correction in the size of the system.

Source: Physical Review Letters

DOI: 10.1103/qxzs-1t1l

Authors: Matteo Gallone, Ricardo Grande, Antonio Ponno, Stefano Ruffo, Erwan Druais

Institutions: Scuola Internazionale Superiore di Studi Avanzati, University of Padua, Istituto Nazionale di Fisica Nucleare, Sezione di Firenze, École Normale Supérieure de Lyon

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,750