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arXiv:cond-mat/9901066 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Confined harmonically interacting spin-polarized fermions in a magnetic field: Thermodynamics

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

Published Apr 1, 1999• 9 citations
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Abstract

We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin-polarized fermions in a confinement potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three-dimensional model of N harmonically interacting spin-polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.

DOI
10.1103/physreve.59.3911

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We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin-polarized fermions in a confinement potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three-dimensional model of N harmonically interacting spin-polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.
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.
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 calculation technique is based on our 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.
We investigate the thermodynamic properties of an ideal charged Bose gas confined in an anisotropic harmonic potential and a constant magnetic field. Using an accurate density of states, we calculate analytically the thermodynamic potential and consequently various intriguing thermodynamic properties, including the Bose–Einstein transition temperature, the specific heat, magnetization, and the corrections to these quantities due to the finite number of particles are also given explicitly. In contrast to the infinite number of particles scenarios, we show that those thermodynamic properties, particularly the Bose–Einstein transition temperature depends upon the strength of the magnetic field due to the finiteness of the particle numbers, and the collective effects of a finite number of particles become larger when the particle number decreases. Moreover, the magnetization varies with the temperature due to the finiteness of the particle number while it keeps invariant in the thermodynamic limit N → ∞ .