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arXiv · 1810.06121

Equilibration of Quasi-Integrable Systems

Tomer Goldfriend·Jorge Kurchan
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Abstract

We study the slow relaxation of isolated quasi-integrable systems, focusing on the classical problem of Fermi-Pasta-Ulam-Tsingou (FPU) chain. It is well-known that the initial energy sharing between different linear-modes can be inferred by the integrable Toda chain. Using numerical simulations, we show explicitly how the relaxation of the FPU chain toward equilibration is determined by a slow drift within the space of Toda's integrals of motion. We analyze the whole spectrum of Toda-modes and show how they dictate, via a Generalized Gibbs Ensemble (GGE), the quasi-static states along the FPU evolution. This picture is employed to devise a fast numerical integration, which can be generalized to other quasi-integrable models. In addition, the GGE description leads to a fluctuation theorem, describing the large deviations as the system flows in the entropy landscape.

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BibTeXRIS

Tomer Goldfriend, Jorge Kurchan. 2018-10-14. Equilibration of Quasi-Integrable Systems. https://doi.org/10.1103/physreve.99.022146

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