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Progress of Theoretical Physics

Partition Functions for Multilevel Parabosonic Systems

Mitsuru Hama, Makoto Sawamura, Hidenori Suzuki

Published Dec 1, 1991• 4 citations
Publisher

Abstract

We calculate the partition functions for the parabosonic systems of level N;;;; order p.The partition functions are compact, independent of p and equivalent to those of the systems of N(N -1) /2 bosonic pairs in addition to N ordinary bosons.We also present a closed form of partition function for two-level parafermion system. § 1. IntroductionMany important properties of para quantum theories l ) have been clarified.2)-7)

DOI
10.1143/ptp.86.1141

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We calculate the partition functions for the parabosonic systems of level N;;;; order p.The partition functions are compact, independent of p and equivalent to those of the systems of N(N -1) /2 bosonic pairs in addition to N ordinary bosons.We also present a closed form of partition function for two-level parafermion system. § 1. IntroductionMany important properties of para quantum theories l ) have been clarified.2)-7)
This study aims to determine the thermodynamic properties of a paraboson system of order two. The thermodynamic properties to be searched include the grand canonical partition function (GCPF), Z , and the average number of particles, N . These parastatistics systems is a more general form compared to a quantum statistical distribution that has been known previously, i.e. Bose-Einstein statistics (BE). Starting from the recursion relation of the GCPF for paraboson system of order two, recursion linkages for some simple thermodynamic functions for paraboson system of order two may be derived. The recursion linkages are then used to calculate the thermodynamic function of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. The results from Z show that the thermodynamics properties of the paraboson system of order two can be derived and have a similar shape with paraboson system of order one (boson). The similarity of the graph shows similar thermodynamic properties.
This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties