Publishing House SB RAS:

Publishing House SB RAS:

Address of the Publishing House SB RAS:
Morskoy pr. 2, 630090 Novosibirsk, Russia



Advanced Search

Journal of Structural Chemistry

2010 year, number 1

Probability of fluctuations of the number of nearest neighbors in A hard sphere liquid: asymptotic decomposition

Y. T. Pavlyukhin
Keywords: asymptotic decompositions in statistic mechanics, hard sphere liquid, simple liquids, liquid with the SW interaction potential
Pages: 65-73

Abstract

Fluctuations of the number of nearest neighbors Mλ inside the coordination sphere of a given radius λ in a hard sphere liquid (Mλ is the total number of neighbors for all N particles of the system) are analyzed. For the probability density distribution of this random value, an exact asymptotic decomposition over the number of particles N in the system has been derived, and the decomposition coefficients were recorded in terms of the semi-invariants of the random value of Mλ. The result coincides completely with the asymptotic decomposition in the central limiting theorem of the probability theory. Due to this, the number of nearest neighbors in a liquid of N hard spheres can be represented as the sum of N independent random values with equal distributions. The hard sphere liquid of N particles was simulated by the Monte Carlo method in the canonical Gibbs ensemble over a wide range of densities (N = 864, periodic boundary conditions, occupancy η from 0.005 to 0.500). The theoretical equations are in good agreement with the results of simulation.