连续相空间和自旋的时间演化：星积和自旋加权球谐函数
Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics
摘要：
我们研究了单自旋的连续相空间，并对它们的时间演化进行了完整的描述。时间演化完全由所谓的星积来描述。我们明确确定这些星产品一般自旋数使用一个简化的方法，适用于自旋加权球谐函数。这种方法自然地将自旋数增加的相空间与它们的量子光学极限联系起来，并允许有效地近似大自旋数的时间演化。我们还近似相空间表示的某些量子态，是具有挑战性的计算大自旋数。所有这些应用程序中探讨了具体的例子，我们概述了扩展耦合自旋系统。
英文摘要：
We study continuous phase spaces of single spins and develop a complete description of their time evolution. The time evolution is completely specified by so-called star products. We explicitly determine these star products for general spin numbers using a simplified approach which applies spin-weighted spherical harmonics. This approach naturally relates phase spaces of increasing spin number to their quantum-optical limit and allows for efficient approximations of the time evolution for large spin numbers. We also approximate phase-space representations of certain quantum states that are challenging to calculate for large spin numbers. All of these applications are explored in concrete examples and we outline extensions to coupled spin systems.
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