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 really localized on few of them. Such a hybrid phase has been recently characterized in other models, such as the Discrete Non-Linear Schr\"odinger equation, just as a finite size effect, while in the low temperature phase of the glassy random laser it seems to be robust in the limit of large size.Comment: 11 pages, 6 figure

Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation: New Proposal

The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical approach to the problem of time, that has the main goal of reproducing quantum field theory on a fixed WKB background accounting also for quantum gravity corrections. We analyze the different choices of the expansion parameter and discuss the problems arising in previous proposals, where a non-unitary evolution emerges as an effect of quantum gravity corrections. In this work we develop a new approach to solve this problem by performing the WKB expansion with the introduction of the so-called kinematical action as a clock for quantum matter, that allows to recover a unitary dynamics.Comment: 24 pages, no figures. Large modification of the paper with the insertion of a new proposa

Universality class of the mode-locked glassy random laser

By means of enhanced Monte Carlo numerical simulations parallelized on GPU's we study the critical properties of the spin-glass-like model for the mode-locked glassy random laser, a $4$-spin model with complex spins with a global spherical constraint and quenched random interactions. Using two different boundary conditions for the mode frequencies we identify the critical points and the critical indices of the random lasing phase transition using , with finite size scaling techniques. The outcome of the scaling analysis is that the mode-locked random laser is in a mean-field universality class, though different from the mean-field class of the Random Energy Model and the glassy random laser in the narrow band approximation, that is, the fully connected version of the present model. The low temperature (high pumping) phase is finally characterized by means of the overlap distribution and evidence for the onset of replica symmetry breaking in the lasing regime is provided.Comment: 15 pages, 11 figure

Nonunitarity problem in quantum gravity corrections to quantum field theory with Born-Oppenheimer approximation

The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical approach to the problem of time, that has the main goal of reproducing quantum field theory on a fixed Wentzel-Kramers-Brillouin (WKB) background accounting also for quantum gravity corrections. We analyze the different choices of the expansion parameter and discuss the problems arising in previous proposals, where a nonunitary evolution emerges as an effect of quantum gravity corrections. In this work, we develop a new approach to solve this problem by performing the WKB expansion with the introduction of the so-called kinematical action as a clock for quantum matter, that allows to recover a unitary dynamics

Realistic model for random lasers from spin-glass theory

This work finds its place in the statistical mechanical approach to light amplification in disordered media, namely Random Lasers (RLs). The problem of going beyond the standard mean-field Replica Symmetry Breaking (RSB) theory employed to find the solution of spin-glass models for RLs is addressed, improving the theory towards a more realistic description of these optical systems. The leading model of the glassy lasing transition is considered: the Mode-Locked (ML) 4 phasor model. This is a complex spherical 4-spin model, with a deterministic selection rule, affecting the coupling of the electromagnetic field modes. The model is investigated with both numerical and analytical techniques