Bifurcations and Chaos in Open Quantum Systems

Timothy P. Spiller, Jason F. Ralph

Anonymous

Mikhail Ivanchenko, Козинов Евгений Александрович, Valentin Volokitin +3 more

Asymptotic state of an open quantum system may change substantially upon variations of system parameters. These changes can be often identified as bifurcation transitions in the classical mean‐filed equations describing evolution of the relevant observables. We demonstrate that these bifurcations can be made visible as changes in the structure of the asymptotic density matrix of the original quantum system. By using an N‐boson dimer, we present quantum ‘bifurcation diagrams’ for the pitchfork and saddle‐node bifurcations (in the stationary dimer) and visualize a period‐doubling transition to chaos (in a periodically modulated dimer).

Titir Mukherjee, Arnab Acharya, Soumitro Banerjee +1 more

Dynamical chaos in a periodically driven, dissipative soft impact oscillator is investigated in the quantum regime using the complex-number quantum Langevin equation (c-number QLE). The averaged system dynamics are analyzed through a comprehensive suite of time-series diagnostics, including bifurcation diagrams, Lyapunov exponents, Fourier spectra, and the 0-1 test. Systematic variation of the wall position reveals a rich sequence of dynamical transitions and grazing bifurcations, progressing from periodic to multiperiodic motion and culminating in chaotic behavior. These results demonstrate the persistence of impact-induced chaos under quantum dissipation and elucidate how environmental fluctuations influence non-linear dynamics in open quantum systems.

Igor Yusipov, S. Denisov, M. V. Ivanchenko

Thomas Dittrich, Robert Graham