The crossover from classical to quantum behavior in Duffing oscillator based on quantum state diffusion |
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Authors: | Y Ota I Ohba |
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Affiliation: | (1) Department of Physics, Waseda University, 169-8555 Tokyo, Japan;(2) Advanced Research Center for Science and Technology, Waseda University, 169-8555 Tokyo, Japan;(3) Kagami Memorial Laboratory for Material Science and Technology, Waseda University, 169-0051 Tokyo, Japan |
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Abstract: | The classical Duffing oscillator is a dissipative chaotic system, and so there is not a definite Hamiltonian. We quantize the Duffing oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can define a ‘Lyapunov exponent’, which corresponds to the classical one in the proper limit, and investigate the behavior of the system by varying the Planck constant effectively. We show that there exists a critical stage, where the behavior of the system crosses over from classical to quantum one. |
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Keywords: | Chaos quantum state diffusion crossover Lyapunov exponent |
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