Classical behavior of systems of quantum oscillators

Carlo Heissenberg, Augusto Sagnotti

Yukihiro Ota, Ichiro Ohba

We discuss the quantum–classical correspondence in a specific dissipative chaotic system, Duffing oscillator. We quantize it on the basis of quantum state diffusion (QSD) that is a certain formulation for quantum open systems and a useful tool for analyzing nonlinear problems and their classical limit. We define a “pseudo-Lyapunov exponent” and investigate the behavior of this quantity varying Planck constant effectively. We show that in a dissipative system there exists some critical stage in which the crossover from classical to quantum behavior occurs. Furthermore, we show that the role of dissipation changes for quantized Duffing oscillator since the effect of dissipation is important for the occurrence of chaos in classical mechanics but suppresses it in quantum region.

Fabio Bagarello

Sergey A. Rashkovskiy

We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system and propose a "classical" explanation of Franck-Hertz experiments.

Thomas Filk A

Yukihiro Ota, Ichiro Ohba

We discuss the quantum-classical correspondence (QCC) in a specific dissipative chaotic system, the Duffing oscillator. The quantum version of the Duffing oscillator is treated as an open quantum system and analyzed numerically by the use of quantum state diffusion (QSD). We consider a pseudo-Lyapunov exponent and investigate it in detail, varying the Planck constant effectively. We show that there exists a critical stage in which the crossover from classical to quantum behavior occurs. Furthermore, we find that a dissipation effect suppresses the occurrence of chaos in the quantum region, while it, combined with the periodic external force, plays a crucial role in the chaotic behavior of the classical system.