Anomalous thermalization of nonlinear wave systems.

We report theoretically and experimentally in an optical system a process of anomalous thermalization of one-dimensional nonlinear Hamiltonian waves. It is characterized by an irreversible evolution of the waves towards a specific equilibrium state of a fundamental different nature than the expected thermodynamic equilibrium state. A kinetic approach of the problem reveals that this phenomenon is due to the existence of a local invariant in frequency space. A novel family of equilibrium distributions is discovered, which is found in quantitative agreement with the numerical simulations.