We study the dynamics of an ensemble of non-interacting harmonic oscillators in a nonlinear dissipative environment described by the Nosé -Hoover model. Using numerical simulation we find the histogram for total energy, which agrees with the analysis of the Nosé -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 α/m, α 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 Nosé -Hoover thermostat.
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