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Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases. (arXiv:1710.02819v1 [cond-mat.quant-gas])

来源于:arXiv
In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult; even the canonical partition function of ideal Bose and Fermi gases cannot be obtained exactly. In this paper, based on the mathematical theory of the symmetric function and the Bell polynomial, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we also reveal that the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods are indeed the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases is calculated from the exact canonical partition function. The virial coefficients of interacting class 查看全文>>