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International Journal of Modern Physics B

THERMODYNAMICS AND PATH INTEGRALS FOR IDENTICAL PARTICLES: THE FORMALISM

F. Brosens, L. F. Lemmens, J. T. Devreese

Published May 10, 2001• 0 citations
Publisher

Abstract

A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function and the static correlation functions of identical particles in a parabolic confining well with harmonic two-body interactions.
DOI
10.1142/s0217979201006318

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A generalization of symmetrized density matrices in combination with the technique of generating functions allows one to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions (repulsive or attractive) are taken into account. Also the influence of a homogeneous magnetic field, introducing anisotropy in the model, is examined. Although the theory is developed for fermions and bosons, special attention is paid to the thermodynamic properties of bosons and their condensation.
Two basic correlation functions are calculated for a model of N harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case. The dependence of these static response properties on the complete range of the temperature and of the number of particles is obtained. The calculation technique is based on the path integral approach of symmetrized density matrices for identical particles in a parabolic confining well.