Structure of hard-hypersphere fluids in odd dimensions

Details Structure of hard-hypersphere fluids in odd dimensions Structure of hard-hypersphere fluids in odd dimensions

2007-08-20

arxiv.org/abs/0708.2677v2

Phys. Rev. E 76, 051202 (2007)

Physics

Condensed Matter

Statistical Mechanics

18 pages, 7 figures; v2: new references added plus minor changes; to be published in PRE

Scientific paper

10.1103/PhysRevE.76.051202

The structural properties of single component fluids of hard hyperspheres in odd space dimensionalities $d$ are studied with an analytical approximation method that generalizes the Rational Function Approximation earlier introduced in the study of hard-sphere fluids [S. B. Yuste and A. Santos, Phys. Rev. A {\bf 43}, 5418 (1991)]. The theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in Laplace space, the coefficients being determined by simple physical requirements. Fourier transform in terms of reverse Bessel polynomials constitute the mathematical framework of this approximation, from which an analytical expression for the static structure factor is obtained. In its most elementary form, the method recovers the solution of the Percus-Yevick closure to the Ornstein-Zernike equation for hyperspheres at odd dimension. The present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state. Excellent agreement with available computer simulation data at $d=5$ and $d=7$ is obtained. As a byproduct of this study, an exact and explicit polynomial expression for the intersection volume of two identical hyperspheres in arbitrary odd dimensions is given.

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