Statistical Mechanics of two hard spheres in a spherical pore, exact analytic results in D dimension

IGNACIO URRUTIA; LESZEK SZYBISZ

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2010 vol. 51 p. 33303 - 33330

0022-2488

This work is devoted to the exact statistical mechanics treatment of simple inhomogeneousfew-body systems. The system of two Hard Spheres (HS) confined into a hard spherical pore is systematically analyzed in terms of its dimensionality D. The canonical partition function, and the one and two-body distribution functions are analytically evaluated and a scheme of iterative construction of the D+1 system properties is presented. We analyse in detail both the efect of high confinement, when particles become caged, and the low density limit. Other confinement situations are also studied analytically and several relations between, the two HS in a spherical pore, two sticked HS into a spherical pore, and two HS on a spherical surface partition functions are traced. These relations make meaningful the limiting caging and low density behavior. The thermodynamic study of the system isdone through the analytical evaluation of the pressure tensor, the equation of state, and the surface tension. The consequences of new results for the two body HS system over the many HS into a spherical pore open system in D dimensions are investigated. New constant coefficients involved in the low density limit properties of the open system are obtained.