自旋1/2系统的相空间旋量振幅
Phase space spinor amplitudes for spin 1/2 systems
摘要：
将连续自由度系统的相空间振幅概念推广到有限维自旋系统。复振幅上获得的球体和有限晶格，在每种情况下，使一个更基本的描述纯自旋状态比以前给出的维格纳函数。在每一种情况下，维格纳函数都可以表示为振幅和它的共轭的星积，因此提供了一个广义的玻恩振幅解释，强调了它们更基本的地位。振幅与其共轭的普通乘积产生（广义）自旋Husimi函数。自旋- $\half$的情况下，详细处理，它示出的相空间振幅的球变换正确的旋量下旋转，尽管他们的表达式在球谐函数。在晶格上的自旋振幅也被发现转化为旋量。应用于态叠加的相空间描述，以及自旋$\half$磁偶极子在含时磁场中的态在相空间中的演化。
英文摘要：
The concept of phase space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-$\half$ is treated in detail, and it is shown that phase space amplitudes on the sphere transform correctly as spinors under under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-$\half$ magnetic dipole in a time-dependent magnetic field.
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