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arXiv:hep-th/9509150 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Canonical partition functions for parastatistical systems of any order

S. Chaturvedi

Published Aug 1, 1996• 24 citations
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Abstract

A general formula for the canonical partition function for a parastatistical system of any order is derived. The formula expresses the canonical partition functions for these in terms of sums of Schur functions.The only hitherto known result due to Suranyi [Phys. Rev. Lett. 65, 2329 (1990)] for parasystems of order two is obtained as a special case. Our results apply not only to parastatistics but to all statistics that can be defined on the basis of the permutation group, including those for which no simple definition in terms of the algebra of creation and annihilation operators is possible. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreve.54.1378

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A general formula for the canonical partition function for a parastatistical system of any order is derived. The formula expresses the canonical partition functions for these in terms of sums of Schur functions.The only hitherto known result due to Suranyi [Phys. Rev. Lett. 65, 2329 (1990)] for parasystems of order two is obtained as a special case. Our results apply not only to parastatistics but to all statistics that can be defined on the basis of the permutation group, including those for which no simple definition in terms of the algebra of creation and annihilation operators is possible. \textcopyright{} 1996 The American Physical Society.
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
Combinatorial aspects of all statistics based on the permutation group are analyzed by imposing the requirements of indistinguishability in the permutation group sense on the Hilbert space describing N identical particles. Compact expressions for the grand canonical partition functions are given wherever possible. The theory of symmetric functions is found to play a significant role in this development. An analysis of the semion statistics of Haldane is also presented from this perspective together with some recent developments in the field of exclusion statistics.
A new formulation of the many-electron correlation problem is presented based on the use of parastatistics. It is shown that second-order para-Fermi creation and annihilation operators, which correspond to the creation and annihilation of spin-averaged paraparticles, occur naturally for the spin-independent many-electron problem. Moreover, the spin-independent many-electron Hamiltonian is directly expressible in terms of the parafield operators. The structure of the general para-Fermi algebra is also investigated from the viewpoint of the pseudo-orthogonal group O(2n+1, 1). Finally, an explicit matrix representation for the para-Fermi algebra of order 2, which enables one to handle even particle-number-nonconserving operators, is obtained in a canonical U(n)-adapted basis.