Wave Turbulence and thermalization in one-dimensional chains

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 at the route of thermalization of 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.

Automated summary

This review highlights the significance of one-dimensional chains as a fundamental model for condensed matter and their contributions to developments in nonlinear physics and complex systems. The pioneering work by Fermi, Pasta, Ulam, and Tsingou in the 1950s laid the foundation for extensive mathematical and physical research in this field over the past 70 years. Recently, the Wave Turbulence approach has provided new insights into the mechanisms of thermalization in such systems. The review critically summarizes the obtained results and identifies open problems and challenges for future investigations.