Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9704040 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Density and pair correlation function of confined identical particles: The Bose-Einstein case

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

Published Jun 1, 1997• 36 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.55.6795

Related papers

THERMODYNAMICS AND PATH INTEGRALS FOR IDENTICAL PARTICLES: THE FORMALISM

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

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.

International Journal of Modern Physics B•May 10, 2001•0 citations

Correlations in a confined gas of harmonically interacting spin-polarized fermions

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

For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for both static responses. The density and the pair correlation function are evaluated explicitly in the ground state of a confined fermion system with a number of particles ranging from 1 to 220, and filling the Fermi level completely.

arXiv:cond-mat/9805379•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Aug 1, 1998•28 citations

Thermodynamics of coupled identical oscillators within the path-integral formalism

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

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.

arXiv:cond-mat/9609108•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 1997•58 citations

Confined harmonically interacting spin-polarized fermions

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

The thermodynamical properties are calculated for a three-dimensional model of $N$ harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy on the complete range of the temperature and of the number of particles turn out to obey a scaling law, similar to the scaling from the continuum approximation for the density of states. The calculational technique is based on our path-integral approach of symmetrized density matrices for identical particles in a parabolic confining well.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Apr 1, 1998•34 citations

Wigner bosonic molecules with repulsive interactions and harmonic confinement

P. Capuzzi, Norman Henry March, Monica Tosi

Abstract In earlier work, the momentum distribution of harmonically confined bosons has been calculated for interparticle interactions which are also harmonic for an arbitrary number N of repelling Bose particles. After a brief discussion of the pair function in this model, attention is also given, but now for N = 2 , to the single-particle density for the repulsive interaction potential λ / r 12 2 , where r 12 is the interboson distance and λ the repulsive coupling strength. The single-particle density is displayed for specific values of λ , with attention focusing on the limit of strong repulsive coupling. Throughout, the focus is on the fingerprints of Wigner bosonic molecules.

World Scientific series in 20th century physics•Sep 1, 2009•0 citations

Pair correlation function of an inhomogeneous interacting Bose-Einstein condensate

Holzmann, M, Yvan Castin

We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte Carlo simulation for various temperatures and compare the numerical result with simple approximative treatments. Around the critical temperature of Bose-Einstein condensation, a description based on the Hartree-Fock approximation is found to be accurate. At low temperatures the Hartree-Fock approach fails and we use a local density approximation based on the Bogoliubov description for a homogeneous gas. This approximation agrees with the simulation results at low temperatures, where the contribution of the phonon-like modes affects the long range behavior of the correlation function. Further we discuss the relation between the pair correlation and quantities measured in recent experiments.

•Jan 1, 1999•13 citations
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.
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.
The thermodynamical properties are calculated for a three-dimensional model of NNN harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy on the complete range of the temperature and of the number of particles turn out to obey a scaling law, similar to the scaling from the continuum approximation for the density of states. The calculational technique is based on our path-integral approach of symmetrized density matrices for identical particles in a parabolic confining well.
Abstract In earlier work, the momentum distribution of harmonically confined bosons has been calculated for interparticle interactions which are also harmonic for an arbitrary number N of repelling Bose particles. After a brief discussion of the pair function in this model, attention is also given, but now for N = 2 , to the single-particle density for the repulsive interaction potential λ / r 12 2 , where r 12 is the interboson distance and λ the repulsive coupling strength. The single-particle density is displayed for specific values of λ , with attention focusing on the limit of strong repulsive coupling. Throughout, the focus is on the fingerprints of Wigner bosonic molecules.
We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte Carlo simulation for various temperatures and compare the numerical result with simple approximative treatments. Around the critical temperature of Bose-Einstein condensation, a description based on the Hartree-Fock approximation is found to be accurate. At low temperatures the Hartree-Fock approach fails and we use a local density approximation based on the Bogoliubov description for a homogeneous gas. This approximation agrees with the simulation results at low temperatures, where the contribution of the phonon-like modes affects the long range behavior of the correlation function. Further we discuss the relation between the pair correlation and quantities measured in recent experiments.