简单非线性系统中的量子Arnol扩散
Quantum Arnol'd Diffusion in a Simple Nonlinear System
摘要：
研究了两个耦合非线性振子在双频外力作用下量子系统中Arnol扩散的指纹。在经典的描述，这种特殊的扩散是由于弱混沌的耦合共振的分界线附近的一个狭窄的随机层的发病。我们已经发现，全球依赖的量子扩散系数模型参数模仿，在一定程度上，经典的数据。然而，量子扩散恰好比经典扩散慢。另一个结果是动态局部化，导致饱和的扩散后，一些特征时间。我们表明，这种效果具有相同的性质，为研究早期的动力学本地化的存在下，全球混沌。量子Arnol'd扩散代表了一种新型的量子动力学，并且可以在例如由时间周期性外部场扰动的2D半导体结构（量子台球）中观察到。
英文摘要：
We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower that the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.
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