Harmonic oscillators in the Nosé-Hoover environment

Abstract

We study the dynamics of an ensemble of noninteracting harmonic oscillators in a nonlinear dissipative environment described by the Nosé-Hoover model, and find the histogram for energy regions of phase space against visiting time by employing numerical simulation. The results agree with the analysis of the Nosé-Hoover equations effected with the method of averaging for small values of the dissipative parameter [Formula presented] of the thermostat. We find oscillations at frequencies proportional to [Formula presented] being the characteristic mass of the particle, about the stationary state corresponding to equilibrium, for sufficiently small [Formula presented]. In this region of [Formula presented] the histogram does not correspond to Gibbs’ canonical distribution. For larger values of [Formula presented] the motion becomes irregular. The phenomena could have an important bearing upon simulating molecular dynamics in the Nosé-Hoover thermostat. © 2004 The American Physical Society.