Harmonic oscillators in the Nos\'e - Hoover thermostat

TL;DR

This paper investigates the dynamics of harmonic oscillators under the Nosé-Hoover thermostat, revealing non-canonical energy distributions and oscillations that impact molecular dynamics simulations.

Contribution

It provides a numerical analysis of oscillator energy histograms and identifies oscillations related to the thermostat's dissipative parameter, offering new insights into the thermostat's behavior.

Findings

Energy histogram deviates from Gibbs distribution

Oscillations occur at frequency proportional to √(α/m)

Results impact understanding of molecular dynamics simulations

Abstract

We study the dynamics of an ensemble of non-interacting harmonic oscillators in a nonlinear dissipative environment described by the Nos\'e - Hoover model. Using numerical simulation we find the histogram for total energy, which agrees with the analysis of the Nos\'e - Hoover equations effected with the method of averaging. The histogram does not correspond to Gibbs' canonical distribution. We have found oscillations at frequency proportional to $\sqrt{\alpha/m}$, $\alpha$ the dissipative parameter of thermostat and $m$ the characteristic mass of particle, about the stationary state corresponding to equilibrium. The oscillations could have an important bearing upon the analysis of simulating molecular dynamics in the Nos\'e - Hoover thermostat.