Abstract
We prove that the stationary BBGKY hierarchy for an infinite system of hard spheres in one dimension has a unique solution for all densities, within a symmetry class that pertains to either a fluid array or to a perfect crystalline array. The solution is shown to correspond to the uniform fluid, which is the only equilibrium state of the infinite system. The proof is subject to the recursion relation for the correlation functions found by Salsburg, Zwanzig, and Kirkwood, which we show exactly reduces the infinite hierarchy to a pair of coupled equations. A brief discussion is given of the existence of multiple solutions of an approximate BBGKY equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Z. W. Salsburg, R. W. Zwanzig, and J. G. Kirkwood,J. Chem. Phys. 21:1098 (1953).
H. J. Raveché and C. A. Stuart,J. Chem. Phys. 65:2305 (1976).
H. J. Raveché and C. A. Stuart,J. Math. Phys. 17:1951 (1976).
F. Gursey,Proc. Camb. Phil. Soc. 46:182 (1950).
L. van Hove,Physica 16:137 (1950).
H. J. Raveché and R. F. Kayser, to be published.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Raveché, H.J., Stuart, C.A. Uniqueness for the BBGKY hierarchy for hard spheres in one dimension. J Stat Phys 17, 311–321 (1977). https://doi.org/10.1007/BF01014401
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01014401