Driven Quantum Many-Body Systems

We advance the theory of quantum Ruelle-Pollicott (RP) resonances and their connection with irreversible relaxation. We relate the spectral form factor to the sum of ensemble-averaged autocorrelation functions and, in generic many-body lattice systems without conservation laws, argue that all quantum RP resonances converge inside the unit disk, highlighting the role of nonunitary and the thermodynamic limit. While we conjecture this picture to be general, we analytically prove the emergence of irreversibility in the random phase model (RPM), a paradigmatic quantum circuit model. To this end, we couple it to arbitrary external local baths and compute the exact time evolution of autocorrelation functions, the dissipative form factor and its partial counterpart, out-of-time-order correlation functions, and operator size. Although the results are valid for any dissipation strength, we then focus on weak dissipation to clarify the origin of irreversibility in the unitary system. When the dissipationless limit is taken after the thermodynamic limit, the unitary quantum map develops an infinite tower of quantum RP resonances inside the unit disk. We trace their microscopic origin to the entropic cost of domain walls in the configuration space of the many-body system. Finally, we demonstrate how conservation laws, many-body localization, and nonlocal interactions cause the leading RP resonance to merge with the unit circle, thereby suppressing the relaxation of the quantities it couples to.