2013/03/05 by T. V. Gevorgyan, A. R. Shahinyan, Lock Yue Chew +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Attractor #Bistability #Chaotic #Classical mechanics #Dissipative system #Limit cycle #Mathematics #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Quantum #Quantum chaos #Quantum decoherence #Quantum dynamics #Quantum mechanics #Statistical physics #cond-mat.supr-con #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.88.022910
published as Phys. Rev. E 88, 022910, 2013 · 10 pages, 14 figures
arxiv created 2013/03/05 · openalex publication_date 2013/08/12 · arxiv updated 2014/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities.