On the Statistics of Many Interacting Waves far from Thermal Equilibrium

The intensity distribution function P(I) for the incoherent superposition of interacting stationary waves far from thermal equilibrium and coupled to many other waves e. g. in active photon and phonon systems is determined analytically for a specific interaction model. The model consists of Nm ⪢ 1 equivalent waves concentrated in a small frequency band which interact through their intensities alone. P{I) refers to Nm′′＜ Nm of these waves. The remaining Nm′=Nm-Nm′′ waves then act as a reservoir. P(l) is shown to be asymptotically given by a Beta-distribution for Nm′⪢ 1. It is found that the interactions thermalize each individual wave which otherwise would be laser like concerning its statistical properties. The photon counting distribution associated with P(l) is also discussed. For Nm′′ comparable to Nm , it can differ significantly from the photon counting distribution of Nm′′ independent thermal waves.