环面结上的费米子
Fermions on a torus knot
摘要：
在这项工作中，我们研究了一个系统考虑\textit{interacting}和\textit{noninteracting}粒子模式，这是限制遵循一个封闭的路径在环面的非平凡的拓扑结构（和几何形状）的影响。为了提出一个突出的物理调查，这个系统的配置，我们进行了详细的分析，使用巨正则系综方法内的统计力学处理\textit{noninteracting}费米子。在分析的方式，我们研究了以下热力学函数在这种情况下：亥姆霍兹自由能，平均能量，磁化强度和磁化率。此外，我们考虑到热力学系统的费米能的行为。最后，我们简要地概述了如何进行的情况下，\textit{interacting}费米子。
英文摘要：
In this work, we investigate the effects of a nontrivial topology (and geometry) of a system considering \textit{interacting} and \textit{noninteracting} particle modes, which are restricted to follow a closed path over the torus surface. In order to present a prominent thermodynamical investigation of this system configuration, we carry out a detailed analysis using statistical mechanics within the grand canonical ensemble approach to deal with \textit{noninteracting} fermions. In an analytical manner, we study the following thermodynamic functions in such context: the Helmholtz free energy, the mean energy, the magnetization and the susceptibility. Further, we take into account the behavior of Fermi energy of the thermodynamic system. Finally, we briefly outline how to proceed in case of \textit{interacting} fermions.
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