高斯和理论的量子地毯
Quantum carpets from Gaussian sum theory
摘要：
在许多封闭的量子系统中，可以观察到一种有趣的现象，称为量子地毯，其中波函数的演化呈现出地毯状的图案。量子地毯的机制类似于光的经典干涉图样。虽然量子地毯的起源以前已经研究过，但仍然有许多有趣的细节值得探索。在这里，我们提出了一个统一的框架，同时分析量子地毯的三个特征，即完全复苏，部分复苏和对角通道。对于分数回复现象，通过高斯和理论给出了一个完整的公式来解释它的产生，该公式可以解析地描述分数回复现象的所有基本特征，包括相位和振幅。此外，我们还揭示了对角运河的干涉项之间的关系和它们的几何解释，提供了一个更好的理解对角运河的形成。
英文摘要：
In many closed quantum systems, an interesting phenomenon, called quantum carpet, can be observed, where the evolution of wave function exhibits a carpet-like pattern. The mechanism of quantum carpet is similar to the classical interference pattern of light. Although the origin of quantum carpets has been studied previously, there are still many interesting details worth exploring. Here, we presented a unified framework for a simultaneous analyzing on three features of quantum carpets, namely full revival, fractional revival and diagonal canal. For fractional revival, a complete formula is presented to explain its generation through "Gaussian sum theory", in which all the essential features, including the phases and amplitudes, of this phenomenon could be captured analytically. Moreover, we also revealed the relations between the interference terms of the diagonal canals and their geometric interpretations, providing a better understanding in the formation of diagonal canals.
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