Equilibration of Quasi-Integrable Systems

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.

13 pages, 9 figures

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• Wave Turbulence and thermalization in one-dimensional chains
• Burgers turbulence in the Fermi-Pasta-Ulam-Tsingou chain
• Universal law of thermalization for one-dimensional perturbed Toda lattices
• Lyapunov spectrum scaling for classical many-body dynamics close to integrability
• Quasi-integrable systems are slow to thermalize but may be good scramblers
• Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit
• Timescales of Chaos in the Inner Solar System: Lyapunov Spectrum and Quasi-integrals of Motion
• Unusual ergodic and chaotic properties of trapped hard rods
• Thermalization of local observables in the $\alpha$-FPUT chain
• Exploring integrability-chaos transition with a sequence of independent perturbations
• The effect of dressing on thermalization of interacting waves
• Thermalization of isolated harmonic networks under conservative noise
• On the role of the Integrable Toda model in one-dimensional molecular dynamics
• Integrable hydrodynamics of Toda chain: case of small systems
• Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities
• Simulating generalised fluids via interacting wave packets evolution
• Large-deviations approach to thermalization: the case of harmonic chains with conservative noise
• Quantum chaos in a harmonic waveguide with scatterers
• Random initial data and average shock time in the Fermi-Pasta-Ulam-Tsingou chain
• Generalised Gibbs Ensemble for spherically constrained harmonic models
• Thermalization in asymmetric harmonic chains
• Thermalization dynamics of macroscopic weakly nonintegrable maps
• Lax dynamics
• Stages of dynamics in the Fermi-Pasta-Ulam system as probed by the first Toda integral