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Physical Review Letters

Thermodynamics of parabosonic and parafermionic systems of order two

P. Surànyi

Published Nov 5, 1990• 18 citations
Publisher

Abstract

The thermodynamics of a gas of order two (Q=2) parabosons or parafermions is shown to be equivalent to that of a mixture of two gases of ordinary bosons or fermions, which either contain equal numbers of particles or the particle numbers of which differ by one.
DOI
10.1103/physrevlett.65.2329

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Hartle and Taylor have shown that the cluster law imposes certain restrictions on the allowed symmetries of first-quantized systems of identical particles. We extend their results to show that all particles which are neither bosons nor fermions and which obey the cluster law can be divided into two classes, those of finite order, and those of infinite order. For every positive integer ppp there are two types of finite-order particle, which we call parabosons and parafermions of order ppp. Ordinary bosons and fermions can be fitted into this scheme as particles of order 1. We conjecture that the finite-order particles can be identified with the parafermions and parabosons of the second-quantized, parafield theory. Infinite-order particles would seem to have no analog in the second-quantized theory, as presently formulated.
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