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

TL;DR

This study uses molecular dynamics simulations to analyze how oscillator chains with onsite anharmonicity relax to equilibrium, comparing results with kinetic theory and revealing insights into energy and phonon density conservation.

Contribution

It provides a detailed comparison between microscopic simulations and Boltzmann-Peierls kinetic theory for anharmonic chains, highlighting quasi-conservation phenomena.

Findings

Quantitative agreement between simulations and kinetic theory after initial transient

Observation of quasi-conservation of phonon density during early relaxation

Evidence of density relaxation to canonical ensemble over long times

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.