On the exact mean-field description of continuous quantum systems in equilibrium

J. Maćkowiak

Physica A: Statistical Mechanics and its Applications, 1983, vol. 117, issue 1, 47-75

Abstract: The thermodynamic limit of free energy density is investigated for quantum systems of n particles obeying Boltzmann, Fermi and Bose statistics, interacting via spin-independent 2-body bounded separable potentials and confined to a bounded region Λ ⊂ Rv. The technique used exploits the Feynman-Kac theorem in finite volume and the saddle-point method of Tindemans and Capel. It is shown that the limiting free energy density of such systems is equal to that of a system of noninteracting particles subject to a mean field which is equal to the averaged 2-body interaction. The equations for the mean field of n particles obeying Boltzmann, Fermi or Bose statistics represent self-consistent field problems and their forms comply with the well-known theorems on mean occupation numbers of single-particle eigenstates of ideal quantum gases at inverse temperature β.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:117:y:1983:i:1:p:47-75

DOI: 10.1016/0378-4371(83)90021-3

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