The Fourth Virial Coefficient for Hard Spheres in Even Dimension
نویسندگان
چکیده
The fourth virial coefficient is calculated exactly for a fluid of hard spheres in even dimensions. For this purpose the complete star cluster integral expressed as sum two three-folded integrals only involving spherical angular coordinates. These are solved anallytically any dimension d and working with existing expressions other terms we obtain an expression B4(d) that sums finite number simple terms, increasing d.
منابع مشابه
The fourth virial coefficient of anyons
We have computed by a Monte Carlo method the fourth virial coefficient of free anyons, as a function of the statistics angle θ. It can be fitted by a four term Fourier series, in which two coefficients are fixed by the known perturbative results at the boson and fermion points. We compute partition functions by means of path integrals, which we represent diagrammatically in such a way that the ...
متن کاملFifth to eleventh virial coefficients of hard spheres.
Virial coefficients B(n) of three-dimensional hard spheres are reported for n=5 to 11, with precision exceeding that presently available in the literature. Calculations are performed using the recursive method due to Wheatley, and a binning approach is proposed to allow more flexibility in where computational effort is directed in the calculations. We highlight the difficulty as a general measu...
متن کاملSecond Virial Coefficient of Anyons without Hard Core
We calculate the second virial coefficient of anyons whose wave function does not vanish at coincidence points. This kind of anyons appear naturally when one generalizes the hard-core boundary condition according to self-adjoint extension method in quantum mechanics, and also when anyons are treated field theoretically by applying renormalization procedure to nonrelativistic ChernSimons field t...
متن کاملOn the relation between virial coefficients and the close-packing of hard disks and hard spheres.
The question of whether the known virial coefficients are enough to determine the packing fraction η(∞) at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes...
متن کاملSimple relationship between the virial-route hypernetted-chain and the compressibility-route Percus-Yevick values of the fourth virial coefficient.
As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus-Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient B(4) predicted by the HNC and PY appro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2022
ISSN: ['0022-4715', '1572-9613']
DOI: https://doi.org/10.1007/s10955-022-02913-7