Quantum-classical correspondence in a nonlinear Gross–Pitaevski system
Quantum-classical correspondence in a nonlinear Gross–Pitaevski system
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DOI：
10.1088/1751-8121/ab1cde
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Wen-Lei Zhao;Jiaozi Wang;Wen-ge Wang
中科院分区：
文献类型：
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作者：
Wen-Lei Zhao;Jiaozi Wang;Wen-ge Wang
研究了由Gross-Pitaevski方程描述的玻色-爱因斯坦凝聚体（BEC）在时间和空间上的周期性非线性相互作用调制下的量子-经典对应.结果表明，该系统等效于广义反冲转子（GKR）模型。有趣的是，随着时间的推移，GKR系统的经典动力学表现出规则到混沌的转变，相应的能量扩散是指数快速的。对于BEC系统，能量扩散可以通过GKR模型的经典映射方程来预测。然而，即使有效普朗克常数很小，BEC系统与经典GKR模型之间的能量比也不是1，这与我们对量子-经典对应的传统理解相矛盾。我们发现BEC系统并不是经典GKR系统的量子对应物。我们构造了一个更好的量子对应物，并导出了能量指数快速扩散的解析表达式，与数值结果完全一致。
We investigate the quantum-classical correspondence of the Bose–Einstein condensate (BEC) which is described by the Gross–Pitaevski equation with the periodic, both temporally and spatially, modulation of nonlinear interaction. It is found that this system is equivalent to a generalized kicked rotor (GKR) model. Interestingly, the classical dynamics of the GKR system exhibits the regular-to-chaotic transition as time evolves, and the corresponding energy diffusion is exponentially fast. For the BEC system, the energy diffusion can be predicted by the classical mapping equation of the GKR model. However, the ratio of the energy between the BEC system and the classical GKR model is not unity, even if the effective Planck constant is very small, which is contradictory to our conventional understanding of quantum-classical correspondence. We find that the BEC system is not exactly a quantum counterpart of the classical GKR system. We construct a better quantum counterpart and derive an analytical expression for the exponentially-fast diffusion of energy, which is in perfect agreement with numerical results.