Wave Turbulence and thermalization in one-dimensional chains

TL;DR

This paper reviews recent advances in understanding thermalization in one-dimensional chains using Wave Turbulence theory, highlighting key results, open problems, and future research directions in nonlinear physics.

Contribution

It provides a comprehensive summary of Wave Turbulence applications to 1D chains and discusses unresolved challenges in the field.

Findings

Wave Turbulence offers insights into thermalization mechanisms.

Identification of open problems in nonlinear chain dynamics.

Critical assessment of recent theoretical developments.

Abstract

One-dimensional chains are used as a fundamental model of condensed matter, and have constituted the starting point for key developments in nonlinear physics and complex systems. The pioneering work in this field was proposed by Fermi, Pasta, Ulam and Tsingou in the 50s in Los Alamos. An intense and fruitful mathematical and physical research followed during these last 70 years. Recently, a fresh look at the mechanisms of thermalization in such systems has been provided through the lens of the Wave Turbulence approach. In this review, we give a critical summary of the results obtained in this framework. We also present a series of open problems and challenges that future work needs to address.