具有混沌势的非线性物质波动力学
Nonlinear Matter Wave Dynamics with a Chaotic Potential
摘要：
我们考虑一个立方非线性薛定谔方程的情况下，与一个额外的混沌潜力，在这个意义上说，这样的潜力产生混沌动力学在经典力学。我们推导并描述了一个适当的半经典限制这样一个非线性薛定谔方程，使用半经典的维格纳函数的解释，并将其与流体动力学限制的Gross-Pitaevskii方程中使用的上下文中的玻色-爱因斯坦凝聚。我们研究了具有这种混沌势的Gross-Pitaevskii方程的一个具体例子：一维Delta-Kicked谐振子及其半经典极限。我们在玻色-爱因斯坦凝聚体实验中探讨了实验实现这样一个系统的可行性，给出了如何实现这样一个配置的具体建议，并考虑了凝聚体耗尽的问题。
英文摘要：
We consider the case of a cubic nonlinear Schrödinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate semiclassical limit to such a nonlinear Schrödinger equation, using a semiclassical interpretation of the Wigner function, and relate this to the hydrodynamic limit of the Gross-Pitaevskii equation used in the context of Bose-Einstein condensation. We investigate a specific example of a Gross-Pitaevskii equation with such a chaotic potential: the one-dimensional delta-kicked harmonic oscillator, and its semiclassical limit. We explore the feasibility of experimental realization of such a system in a Bose-Einstein condensate experiment, giving a concrete proposal of how to implement such a configuration, and considering the problem of condensate depletion.
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