Dissipative Quantum Chaos

Abstract
Describing complex interacting quantum systems is a daunting task. Over the past 60 years, tools originating from such disparate areas as neutron scattering, mesoscopic transport, or quantum chromodynamics, fuelled the emergence and development of the field of quantum chaos with exactly this goal in mind. Arguably, one of its most spectacular achievements was the identification of universal signatures of chaos in quantum systems, characterizing the correlations of their energy levels. We will give a broad overview of the signatures of quantum chaos in closed (Hamiltonian) quantum systems, with special emphasis on the distribution of energy spacings. We then move to quantum systems in contact with an environment, where dissipation and decoherence coexist with unitary dynamics.

We outline the main questions of this emerging field, explain what difficulties arise when combining dissipation with quantum chaos, and how to overcome them. In particular, we discuss our recent proposal of using complex spacing ratios as a signature of dissipative quantum chaos.