Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory

Abstract

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasi-conservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On super-kinetic time scales, density quasi-conservation is lost while energy remains conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. However, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.

arXiv comment9 pages, 11 figures

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Cited by in corpus (6)

• Nonintegrability and thermalization of one-dimensional diatomic lattices
• Pre-thermalization in a classical phonon field: slow relaxation of the number of phonons
• Effect of pressure on thermalization of one-dimensional nonlinear chains
• The anti-Fermi-Pasta-Ulam-Tsingou problem in one-dimensional diatomic lattices
• Controllability in tunable chains of coupled harmonic oscillators
• Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds