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Physical Review A

Quantum third virial coefficient of a fractional-statistics gas

J. Law, Akira Suzuki, R. K. Bhaduri

Published Oct 1, 1992• 15 citations
Publisher

Abstract

A quantum calculation of the third virial coefficient of a two-dimensional gas obeying fractional statistics is performed by diagonalizing the three-body Hamiltonian in a harmonic-oscillator potential with a large fermionic basis. The numerical results for the virial coefficient ${\mathit{A}}_{3}$ as a function of the flux strength \ensuremath{\alpha} (\ensuremath{\alpha}=0 for fermions, \ensuremath{\alpha}=1 for bosons) are reliable in the range 0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}0.25. $A sub 3--- increases quadratically with \ensuremath{\alpha} for very small \ensuremath{\alpha}, but higher powers contribute substantially for large \ensuremath{\alpha}.

DOI
10.1103/physreva.46.4693

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For three anyons confined in a harmonic oscillator, only the class of states that interpolates nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full three-body partition function as was done in an earlier publication [J. Law, A. Suzuki, and R. Bhaduri, Phys. Rev. A 46, 4693 (1992)], here only the nonlinear contribution is calculated, thus avoiding delicate cancellations between the irrelevant linear part and the two-body partition function. Our numerical results are consistent with the simple analytical form suggested recently by Myrheim and Olaussen [Phys. Lett. B 299, 267 (1993)].
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Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in ddd dimension and the equivalence of trapped quantum gases
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