FPU phenomenon for generic initial data

Abstract

The well known FPU phenomenon (lack of attainment of equipartition of the mode--energies at low energies, for some exceptional initial data) suggests that the FPU model does not have the mixing property at low energies. We give numerical indications that this is actually the case. This we show by computing orbits for sets of initial data of full measure, sampled out from the microcanonical ensemble by standard Montecarlo techniques. Mixing is tested by looking at the decay of the autocorrelations of the mode--energies, and it is found that the high--frequency modes have autocorrelations that tend instead to positive values. Indications are given that such a nonmixing property survives in the thermodynamic limit. It is left as an open problem whether mixing obtains within time--scales much longer than the presently available ones.

References in corpus (3)

• The Fermi-Pasta-Ulam problem: 50 years of progress
• Weak and strong chaos in FPU models and beyond
• Slow relaxation, confinement, and solitons

Cited by in corpus (10)

• Equilibration of Quasi-Integrable Systems
• The Fermi-Pasta-Ulam problem and its underlying integrable dynamics: an approach through Lyapunov Exponents
• An averaging theorem for FPU in the thermodynamic limit
• An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit
• A series expansion for the time autocorrelation of dynamical variables
• Structural localization in the Classical and Quantum Fermi-Pasta-Ulam Model
• Universal route to thermalization in weakly-nonlinear one-dimensional chains
• Nonlinear dynamics determines the thermodynamic instability of condensed matter in vacuo
• Stages of dynamics in the Fermi-Pasta-Ulam system as probed by the first Toda integral
• Comparison between different methods of estimating of the relaxation times in the FPU model