Abstract:
An ensemble of nonlinear classical oscillators in a thermal bath and in the field of
an harmonic external force is considered. Systematic application of the method of
averaging with respect to the fast variables makes it possible to obtain approximate analytic solutions for the distribution function in a steady regime in different regions of the phase space separated by a separatrix. Matching of the solutions belonging to different regions of the phase space confirms the conjecture that there is an excess population in the region of oscillator energies in which the frequency of the eigenmodes of the oscillator is close to the frequency of the external force.
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