有限维离散相空间的准概率分布函数：玩具模型中的自旋隧道效应
Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model
摘要：
我们展示了如何准概率分布函数定义在$N^{2}$维离散相空间可以用来治疗物理系统所描述的一个有限的状态空间表现出自旋隧道效应。然后将这种特殊的方法应用于Lipkin-Meshkov-Glick模型，以获得离散Husimi函数的时间演化，并作为副产品的基态和第一激发态的对称组合的能隙。此外，我们还展示了如何一个角度为基础的潜在的方法可以有效地用来解释定性的自旋隧道的能隙的某些功能。熵泛函也在这方面进行了讨论。这样的结果不仅加强了形式本身，而且在物理学的其他分支的一些未来的潜在应用的可能性。
英文摘要：
We show how quasiprobability distribution functions defined over $N^{2}$-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin tunneling effects. This particular approach is then applied to the Lipkin-Meshkov-Glick model in order to obtain the time evolution of the discrete Husimi function, and as a by-product the energy gap for a symmetric combination of ground and first excited states. Moreover, we also show how an angle-based potential approach can be efficiently employed to explain qualitatively certain features of the energy gap in terms of a spin tunneling. Entropy functionals are also discussed in this context. Such results reinforce not only the formalism per se but also the possibility of some future potential applications in other branches of physics.
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