On the exact mean-field description of continuous quantum systems in equilibrium
The author investigates the thermodynamic limit of a quantum continuous system with separable 2-body interactions. The choice of separable potentials makes it possible to consider the continuous analogue of the mean field approximation used in the investigation of lattice systems. The condition of separability is rather unrealistic though the assumption that the potentials be in \(L^{\infty}(R^{\nu})\) can be considerable relaxed. The proof of the existence of the thermodynamic limit is based on the Feynman-Kac formula and Bogolyubov inequality. The mean field approximation is obtained by extending the saddle point method used by \textit{P. A. J. Tindemans} and \textit{H. W. Capel} [Physica A 85, 435 ff (1974)]. Particles obeying Boltzmann, Fermi-Dirac and Bose-Einstein statistics are treated. The author shows that the mean field approximation is exact in the sense that the thermodynamic limit of the free energy density coincides with the thermodynamic limit of the free energy density of a system of free paricles subject to an external field equal to the averaged two body interaction.
Boltzmann, Fermi-Dirac and Bose-Einstein statistics
scientific article; zbMATH DE number 3846911
scientific article