Glassy behavior of light in random lasers

A theoretical analysis [Angelani , Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behavior of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very general equations (that also apply to other systems, like Bose-Condensed gases) describing light in a disordered nonlinear medium and through some approximations we relate them to a mean-field spin-glass-like model. The model is solved by the replica method, and replica-symmetry breaking phase transition is predicted. The transition describes a mode-locking process in which the phases of the modes are locked to random (history and sample-dependent) values. An extended discussion of possible experimental implications of our analysis is reported.