Spectral gaps and dynamical transitions in random open quantum systems

The way nonequilibrium systems relax to their steady states is the subject of extensive research. This talk addresses the universal features of such dynamics in open quantum systems. Specifically, I will discuss the relaxation rate of a chaotic quantum system coupled to noise, using a random matrix model where both the Hamiltonian and the system-noise coupling exhibit power-law distance dependence. I will demonstrate the existence of three distinct dynamical phases, characterized by the behavior of the spectral gap of the Liouvillian superoperator that generates the dynamics. One phase is gapped and relaxation is asymptotically exponential. Conversely, the other two phases are gapless and exhibit subexponential relaxation, distinguished by the scaling of the vanishing gap with system size. I will also describe several spectral features emerging in the limits of weak and strong decoherence.