On the exact mean-field description of continuous quantum systems in equilibrium
type: Item
instance of: scholarly article
title: On the exact mean-field description of continuous quantum systems in equilibrium
zbMATH Open document ID: 0533.70013
DOI: 10.1016/0378-4371(83)90021-3
author: Jan Maćkowiak
published in: Physica A
publication date: 1983-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76G25
Mathematics Subject Classification ID: 82B10
Mathematics Subject Classification ID: 82B20
zbMATH DE Number: 3846911
zbMATH Keywords: thermodynamic limit
zbMATH Keywords: quantum continuous system
zbMATH Keywords: separable 2-body interactions
zbMATH Keywords: mean field approximation
zbMATH Keywords: Feynman-Kac formula
zbMATH Keywords: Bogolyubov inequality
zbMATH Keywords: saddle point method
zbMATH Keywords: Boltzmann, Fermi-Dirac and Bose-Einstein statistics
zbMATH Keywords: free energy density
MaRDI profile type: Publication
full work available at URL: 0378-4371(83)90021-3
OpenAlex ID: W4235487882
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description: scientific article; zbMATH DE number 3846911