Intensity pseudo-localized phase in the glassy random laser

Evidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor strictly condensed on few of them. Such a hybrid phase, recently characterized as a finite size effect in other models, such as the discrete non-linear Schrödinger equation, in the low temperature phase of the glassy random laser appears to be robust in the limit of large size.