Wave Turbulence and thermalization in one-dimensional chains

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.

arXiv admin note: text overlap with arXiv:1811.05697 by other authors

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• Periodic Orbits in Fermi-Pasta-Ulam-Tsingou Systems
• The effect of dressing on thermalization of interacting waves
• Dynamical and structural properties of an absorbing phase transition: a case study from granular systems
• Three- and four-wave resonances in the nonlinear quadratic Kelvin lattice
• A general multi-wave quasi-resonance theory for lattice energy diffusion
• Spatio-temporal thermalization and adiabatic cooling of guided light waves
• Adiabatic Gauge Potential as a Tool for Detecting Chaos in Classical Systems
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• Irreversible thermalization vs reversible dynamics mediated by anomalous correlators: Wave turbulence theory and experiments in optical fibers
• Thermalization in asymmetric harmonic chains