Ota Yukihiro, Ohba Ichiro
Department of Physics, Waseda University, Tokyo 169-8555, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jan;71(1 Pt 2):015201. doi: 10.1103/PhysRevE.71.015201. Epub 2005 Jan 7.
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.
我们讨论了特定耗散混沌系统——杜芬振子中的量子-经典对应（QCC）。杜芬振子的量子版本被视为一个开放量子系统，并通过量子态扩散（QSD）进行数值分析。我们考虑了一个伪李雅普诺夫指数，并通过有效改变普朗克常数对其进行了详细研究。我们表明，存在一个从经典行为到量子行为发生转变的临界阶段。此外，我们发现耗散效应抑制了量子区域中混沌的出现，而它与周期性外力相结合，在经典系统的混沌行为中起着关键作用。
