Shen Yao, Zhao Yu-Lin
School of Criminal Science and Technology , People's Public Security University of China , Beijing 100038 , China.
Department of Physics , Tianjin University , Tianjin 300350 , China.
J Phys Chem A. 2018 Aug 2;122(30):6349-6353. doi: 10.1021/acs.jpca.8b05121. Epub 2018 Jul 25.
Gentile statistics, which is famous for its advantages in dealing with composite particle systems, is a kind of fractional statistics. Lately, researchers are concentrating on finding real systems that obey Gentile statistics. Five years ago, we discovered that the cyclic hydrocarbon polyenes called N-annulenes in the Hückel model had certain correspondence with Gentile oscillators. According to their rotation and dihedral symmetry, these two systems had the same energy levels and partition functions. In this paper, we give further discussions. We discuss the transformations of wave functions between N-annulenes and Gentile oscillators, the creation and annihilation operators in site pictures of N-annulenes, the coherent state, and the mathematical proofs of the intermediate commutation relations of operators. All of our works prove that N-annulenes in the Hückel model are real Gentile statistical systems and offer a new algebraic method to deal with the problems of electron-electron and electron-phonon interactions.
简并统计以其在处理复合粒子系统方面的优势而闻名，是一种分数统计。最近，研究人员正专注于寻找服从简并统计的真实系统。五年前，我们发现休克尔模型中称为N - 轮烯的环状烃多烯与简并振子有一定的对应关系。根据它们的旋转和二面角对称性，这两个系统具有相同的能级和配分函数。在本文中，我们给出进一步的讨论。我们讨论了N - 轮烯和简并振子之间波函数的变换、N - 轮烯格点图中的产生和湮灭算符、相干态以及算符中间对易关系的数学证明。我们所有的工作都证明了休克尔模型中的N - 轮烯是真实的简并统计系统，并提供了一种新的代数方法来处理电子 - 电子和电子 - 声子相互作用的问题。
