Instabilities and relaxation to equilibrium in long-range oscillator chains

Abstract

We study instabilities and relaxation to equilibrium in a long-range extension of the Fermi-Pasta-Ulam-Tsingou (FPU) oscillator chain by exciting initially the lowest Fourier mode. Localization in mode space is stronger for the long-range FPU model. This allows us to uncover the sporadic nature of instabilities, i.e., by varying initially the excitation amplitude of the lowest mode, which is the control parameter, instabilities occur in narrow amplitude intervals. Only for sufficiently large values of the amplitude, the system enters a permanently unstable regime. These findings also clarify the long-standing problem of the relaxation to equilibrium in the short-range FPU model. Because of the weaker localization in mode space of this latter model, the transfer of energy is retarded and relaxation occurs on a much longer time-scale.

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Cited by in corpus (3)

• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• The fifth-order partial differential equation for the description of the α+β Fermi-Pasta-Ulam model
• Pulse solutions of the fractional effective models of the Fermi-Pasta-Ulam lattice with long-range interactions