Effects of a finite number of particles on the thermodynamic properties of a noninteracting trapped Fermi gas

摘要

The effects of a finite number of particles on the thermodynamic properties of a noninteracting Fermi gas trapped in a harmonic potential are investigated. The expressions of a series of thermodynamic quantities, which include the chemical potential, total energy and heat capacity, are derived analytically, and the corrections to these quantities due to the finite number of particles are given explicitly. It is found that the first order corrections from the finite number of particles are exactly cancelled by the corrections from the zero-point energy, so that the collective effects of a finite number of particles and zero-point energy are very small. This is different from the effects of a finite number of particles on the properties of a Bose gas. Moreover, it is shown that the analytical results obtained here are in excellent agreement with those given by the exact numerical calculation. (C) 2004 Elsevier B.V. All rights reserved.