Quantum chaos studies chaotic behavior in quantum systems. Researchers extend this concept to open quantum systems. Open systems interact with environments. Therefore, they experience dissipation and decoherence.
In closed systems, quantum chaos shows level repulsion. Energy levels follow random matrix theory statistics. Moreover, out-of-time-order correlators reveal information scrambling.
However, open systems use non-Hermitian operators. The Liouvillian superoperator governs dynamics. Researchers analyze its complex eigenvalues. Chaotic open systems display level repulsion in complex plane. Integrable ones show Poisson-like clustering.
Furthermore, complex spacing ratios serve as key diagnostics. These ratios distinguish chaos from integrability. Studies apply them to dissipative many-body systems.
Additionally, quantum trajectories highlight chaos. Stochastic realizations show extreme sensitivity. Dissipative effects combine with Hamiltonian chaos. Thus, chaos emerges even in steady states.
Krylov complexity acts as another probe. It uses bi-Lanczos methods. This tool reliably identifies chaotic phases in open systems. It aligns with spectral statistics and Ginibre ensemble predictions.
Spectral form factors also adapt to open cases. They decay exponentially first. Then, they plateau or show other behaviors. These patterns reveal scrambling under dissipation.
Recent works explore thermalization in open systems. Researchers propose Liouvillian ETH analogs. Local operators behave statistically like in closed chaotic cases.
Overall, quantum chaos in open systems bridges theory and experiment. It advances quantum thermodynamics and computing. Dissipation modifies but does not eliminate chaotic signatures. Researchers continue to uncover universal features through spectral analysis and trajectory studies.