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

We consider a system of externally pumped nonequilibrium harmonic oscillato rs (vibrational modes) interacting through anharmonic effects with a system of harmonic oscillators with lower-lying frequencies (acoustic-like vibrat ions) composing a thermal bath for the former. We derive the equations of e volution for the population of the vibrational modes, introducing high orde r nonlinear relaxation processes. It is shown that complex behavior arises in this system, namely, after a certain critical intensity of the pumping s ource is achieved, the populations of the modes lowest in frequency increas e 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. (C) 2000 Elsevier Science Ltd. All rights reserved.