Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

Abstract

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.\textbf{ }In this paper, based on the mathematical theory of the symmetric function, 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 express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of 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 classical and quantum gases is calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

References in corpus (6)

• Condensation of Ideal Bose Gas Confined in a Box Within a Canonical Ensemble
• Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice
• Intermediate-statistics quantum bracket, coherent state, oscillator, and representation of angular momentum (su(2)) algebra
• The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries
• Effective approach for taking into account interactions of quasiparticles from the low-temperature behavior of a deformed fermion-gas model
• The microscopic meaning of grand potential resulting from combinatorial approach to a general system of particles

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• Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework
• Bose-like few-fermion systems
• Unified framework for generalized quantum statistics: canonical partition function, maximum occupation number, and permutation phase of wave function
• Scattering approach for calculating one-loop effective action and vacuum energy
• Heat kernel approach for confined quantum gas