Quantum counterpart of equipartition theorem: A Möbius inversion approach

Xin-Hai Tong, Yao Wang
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Abstract

The equipartition theorem is crucial in classical statistical physics, and recent studies have revealed its quantum counterpart for specific systems. This raises the question: does a quantum counterpart of the equipartition theorem exist for any given system, and if so, what is its concrete form? In this Letter, we employ the Möbius inversion approach to address these questions, providing a criterion to determine whether a system adheres to the quantum counterpart of the equipartition theorem. If it does, the corresponding distribution function can be readily derived. Furthermore, we construct the fermionic version of the criterion in a manner analogous to the bosonic case.

Abstract Image

等分定理的量子对应物:莫比乌斯反演法
等分定理在经典统计物理学中至关重要,最近的研究揭示了特定系统的量子对应定理。这就提出了一个问题:对于任何给定系统,是否存在等分定理的量子对应定理?在这封信中,我们采用莫比乌斯反演法来解决这些问题,提供了一个标准来确定一个系统是否遵守等分定理的量子对应定理。如果符合,就可以很容易地推导出相应的分布函数。此外,我们还以类似于玻色子的方式构建了该准则的费米子版本。
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CiteScore
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