Harmonic oscillators in the Nosé-Hoover environment.

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 alpha of the thermostat. We find oscillations at frequencies proportional to sqrt[alpha/m ], m being the characteristic mass of the particle, about the stationary state corresponding to equilibrium, for sufficiently small alpha . In this region of alpha the histogram does not correspond to Gibbs' canonical distribution. For larger values of alpha the motion becomes irregular. The phenomena could have an important bearing upon simulating molecular dynamics in the Nosé-Hoover thermostat.