Cancelled Spectral gaps and dynamical transitions in random open quantum systems

The relaxation of nonequilibrium systems to their steady states, and especially the universal
features of such dynamics, is of considerable interest. In this talk I will discuss the relaxation
rate of a chaotic quantum system coupled to noise, using a model where the Hamiltonian and the
system-noise coupling are described by random matrices whose entries decay as power laws of distance.
I will show that the rate exhibits three phases depending on the exponents of the power laws:
a phase where the approach is asymptotically exponential as a result of a gap in the spectrum of the
Liouvillian superoperator that generates the dynamics, and two gapless phases with subexponential
relaxation, distinguished by the manner in which the gap decreases with system size. I will also
describe several spectral features emerging in the limits of weak and strong decoherence.