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Virial coefficients and equation of state of hard-core fluids in d-dimensions

By: Mariano López de Haro
From: Departamento de Física, Universidad de Extremadura, E-06071 Badajoz, Spain
At: Complexo Interdisciplinar, Anfiteatro
[2009-05-27] 12:00

In this talk I will discuss the convergence properties of the virial series of hard-core fluids in d-dimensions. First, using the results of a recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E. 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick (PY) equation for a fluid of hard spheres in (odd) d dimensions, I will consider the equations of state of these systems derived through the virial and the compressibility routes. In both cases, the virial coefficients b_j turn out to be expressed in terms of the solution of a set of (d - 1)/2 coupled algebraic equations which become nonlinear for d ≥ 5 and I will show results derived up to d = 13. These confirm the alternating character of the series of the PY theory for d ≥ 5, due to the existence of a branch point on the negative real axis, which in turn allows one to obtain the corresponding radius of convergence for each dimension. The resulting scaled density per dimension 2η^1/d, where η is the packing fraction, is wholly consistent with the limiting value of 1 for d o ∞. Next, using the first seven known (exact) virial coefficients [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)] and forcing it to possess two branch-point singularities, I will introduce a new proposal for the equation of state of hard-core fluids in d-dimensions. For d = 3 this equation of state predicts accurate values of the higher virial coefficients, a radius of convergence smaller than the close-packing value and it is as accurate as the rescaled virial expansion or the Pade [3/3] equations of state. Finally, I will point out some possible consequences regarding the convergence properties of the true virial series.