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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Confined harmonically interacting spin-polarized fermions

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

Published Apr 1, 1998• 34 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.57.3871

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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.
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.
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.
The thermodynamics of the inhomogeneous one-dimensional repulsive fermionic Hubbard model with parabolic confinement is studied by a density-functional-theory approach, based on Mermin's generalization to finite temperatures. A local-density approximation (LDA), based on exact results for the homogeneous model, is used to approximate the correlation part in the Helmholtz free-energy, comprising the thermodynamic Bethe ansatz LDA (TBALDA). The general presentation of the method is given and some properties of the homogeneous model that are relevant to the DFT approach are analyzed. Extensive comparison between TBALDA and numerical exact diagonalization results for thermodynamic properties of small inhomogeneous chains is discussed. In the remaining, a classical thermodynamic treatment of the confined system is developed with the focus on global properties of large systems. It is observed that, depending on the temperature and specific volume, the system can have its temperature increased under isentropic expansion. Such unusual behavior becomes more pronounced with the increase of the intrasite interaction UUU and can be understood considering the peculiar behavior of the correlation entropy per site of the Hubbard model around half-filling. A related nonmonotonic variation of the temperature under isentropic change of UUU is also studied. At the end, the dependence of the double occupancy on temperature and volume per particle is discussed.
We calculate the quantum corrections of the thermodynamic quantities of a system of confined bosons at finite temperature. Systematically quantum corrections are written in a series of $\ensuremath{\Elzxh},$ which is convergent when kT\mathrm{kT}kT is much larger than the spacing between energy levels of the system. We apply this method to the different physical systems. First we calculate the thermodynamic potential of spin-1 bosons confined in a general power-law potential, and calculate the paramagnetic susceptibility of the gas including the quantum corrections. Local-density approximation for charged bosons in the weak magnetic field is improved by the semiclassical expansion. Diamagnetic susceptibility of a system of confined charged bosons is calculated using this method. Finally we apply this method to calculate analytically the thermodynamic potential of a weakly interacting Bose-gas confined in at three-dimensional harmonic-oscillator potential. For a large number of particles, quantum corrections become small, and contribute to the finite-size corrections to scaling.