MONTE-CARLO SIMULATION OF THE HARD-SPHERE FLUID WITH A HIGH-TEMPERATURE QUANTUM CORRECTION IN THE REGION OF THE FLUID SOLID-PHASE TRANSITION

Abstract

Monte Carlo simulations have been carried out for the hard-sphere system in the region of the fluid-solid phase transition with a quantum mechanical correction. The two-body Slater sum has been used as the quantum mechanical probability in the configurational space rather than the classical Boltzmann distribution function. The internal energy and the pressure depend not only on the density, but also on the thermal wavelength which is a function of the mass and temperature, while the classical results depend only on the density. These thermodynamic quantities are greater, in general, in the quantum mechanical treatment than in the classical one. The correction term in the compressibility factor is about 40% of the classical value in the phase transition region when the ratio of the thermal wavelength to the hard-sphere diameter is 0.1; as the quantum effect increases, the region of the phase transition appears at lower density. Two kinds of equation of state are presented, one for the solid branch and one for the fluid branch of the quantum mechanical hard-sphere system, by using the classical expressions but replacing the classical hard-sphere diameter by the effective diameter.