Quantifying dissipative quantum chaos

Irregular, chaotic dynamics of nonlinear systems is deeply studied and well understood. Dynamical chaos also arises in the classical approximation of quantum systems, modeled by nonlinear differential equations. However, quantum systems can either be in an essentially non-classical regime, or not allow a classical description at all. Here lies the terra incognita of modern physics of complex systems: can linear (by definition) mathematical models of dissipative quantum systems exhibit the properties of nonlinear chaotic systems (probably yes - as suggested by the correspondence principle)? What are the "fingerprints" of classical deterministic chaos in these systems? How can one "see" quantum bifurcations and measure dissipative quantum chaos? The answers to these questions are not only of fundamental interest, but are also extremely important in the field of quantum computing for solving the problem of stable processing of quantum information on long time scales.