Nonlinear relaxation in nonequilibrium oscillators: Bose–Einstein-like condensation in a dissipative structure

We consider a system of externally pumped nonequilibrium harmonic oscillators (vibrational modes) interacting through anharmonic effects with a system of harmonic oscillators with lower-lying frequencies (acoustic-like vibrations) composing a thermal bath for the former. We derive the equations of evolution for the population of the vibrational modes, introducing high order nonlinear relaxation processes. It is shown that complex behavior arises in this system, namely, after a certain critical intensity of the pumping source is achieved, the populations of the modes lowest in frequency increase enormously at the expense of the excitations of the other modes. In this way there follows what can be termed a Bose–Einstein-like condensation, not in a phase in equilibrium, but in a nonequilibrium dissipative structure.