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arXiv 1607.01604quant-ph
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非均匀介质平板几何中的Lévy输运

Lévy Transport in Slab Geometry of Inhomogeneous Media

Alexander Iomin, Trifce Sandev

摘要:

我们提出了一个物理例子,其中分数(在空间和时间)薛定谔方程出现只是作为一个形式的有效描述复杂的非均匀介质中的扩散波输运。这种描述是对应于分数亥姆霍兹方程的傍轴小角度近似的抛物方程近似的结果。所得到的有效量子动力学在空间和时间上都是分数的。作为一个例子,Lévy飞行在一个无限大的势阱被认为是数值。并得到了量子动力学有效波函数的解析表达式。

英文摘要:

We present a physical example, where a fractional (both in space and time) Schrödinger equation appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media. This description is a result of the parabolic equation approximation that corresponds to the paraxial small angle approximation of the fractional Helmholtz equation. The obtained effective quantum dynamics is fractional in both space and time. As an example, Lévy flights in an infinite potential well are considered numerically. An analytical expression for the effective wave function of the quantum dynamics is obtained as well.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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