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

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  • Maćkowiak, J.

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.

Suggested Citation

  • Maćkowiak, J., 1983. "On the exact mean-field description of continuous quantum systems in equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(1), pages 47-75.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:1:p:47-75
    DOI: 10.1016/0378-4371(83)90021-3
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    References listed on IDEAS

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    1. den Ouden, L.W.J. & Capel, H.W. & Perk, J.H.H. & Tindemans, P.A.J., 1976. "Systems with separable many-particle interactions. I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(1), pages 51-70.
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