Liouvillian spectral collapse in the Scully-Lamb laser model

Phase transitions of thermal systems and the laser threshold were first connected more than forty years ago. Despite nonequilibrium nature laser, Landau theory phase transitions, applied directly to Scully-Lamb model (SLLM), indicates that is a second-order transition, associated with $U(1)$ spontaneous symmetry breaking (SSB). To capture genuine transition SLLM (i.e., single-mode without saturable absorber), here we employ quantum dissipative transitions. Our results confirm SSB can occur at lasing but, in contrast semiclassical approximation, they signal "fundamental" different phenomenon, which call Liouvillian spectral collapse; is, emergence diabolic points infinite degeneracy. By considering generalized additional dephasing, witness collapse, but absence breaking. Most surprisingly, corresponds dynamical multistability even SSB. Normally, bistability suppressed by fluctuations, while this case, very presence fluctuations enables bistability. This rather anomalous bistability, characterizing truly origin lasing, be an experimental signature our predictions, show it emergent hysteresis.