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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
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