Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions

Abstract

We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyper-spheres in dimensions $d=4,6$ and 8, and find good agreement with available exact results and Monte-Carlo simulations. This paper confirms the alternating character of the virial series for $d\ge 6$, and provides the first evidence for an alternating character for $d=4$. Moreover, we show that this sign alternation is due to the existence of a branch point on the negative real axis. It is this branch point that determines the radius of convergence of the virial series, whose value we determine explicitly for $d=4,6,8$. Our results complement, and are consistent with, a recent study in odd dimensions [R.D. Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)].

Accepted for publication in J. Chem. Phys. (11 pages, 6 figures)

References in corpus (11)

• Packing Hyperspheres in High-Dimensional Euclidean Spaces
• Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
• Analytic calculation of B4 for hard spheres in even dimensions
• New results for virial coefficients of hard spheres in D dimensions
• Negative virial coefficients and the dominance of loose packed diagrams for D-dimensional hard spheres
• Structure of hard-hypersphere fluids in odd dimensions
• The fourth virial coefficient of a fluid of hard spheres in odd dimensions
• Solution of the Percus-Yevick equation for hard discs
• Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations
• Virial series for fluids of hard hyperspheres in odd dimensions
• Percus-Yevick theory for the structural properties of the seven-dimensional hard-sphere fluid

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