Bifurcations and Chaos in Open Quantum Systems

A study of open quantum systems and dynamical regimes that emerge in such systems is an actively developing field of the theoretical and experimental physics. Although the bifurcation analysis and the theory of dynamical chaos are very important branches of nonlinear dynamics, their use for describing the processes occurring in open dissipative quantum systems has been restricted until recently. In this work, we present a review of recent results on the generalization of the methods of the oscillation theory for such systems. We present quantum analogs of the classical bifurcations, which are observed in the structural changes of the asymptotic density matrix, namely, the pitchfork bifurcation, saddle-node bifurcation, transition to quantum chaos via a period-doubling cascade, and the Neimark-Sacker bifurcation. We also consider numerical characteristics of dissipative quantum chaos. The largest quantum Lyapunov exponent, which is based on analyzing the divergence rate of the initially close quantum trajectories, allows one to numerically study the structure of the regular and chaotic domains of various open quantum systems. Numerical characteristics of dissipative quantum chaos, which can be observed in a physical experiment, are also considered. It is shown that the qualitatively different statistics of the distribution of times between the successive emissions of individual photons by the system take place for the regular and chaotic regimes in an open quantum cavity.