Condensation in Hamiltonian Parametric Wave Interaction

In the generic Hamiltonian problem of parametric wave interaction, we show theoretically the existence of a sudden transition leading the wave system from completely incoherent states towards highly coherent states. This self-organization process is characterized by a reduction of the nonequilibrium entropy, in contrast with the $H$ theorem of entropy growth inherent to the random phase approximation approach. The mechanism underlying this intriguing condensation process is in essence a reversible nonlinear damping. As a result, the lower the coherence of the initial state, the higher the coherence of the final state.