Confined Harmonically Interacting Spin-Polarized Fermions in a Magnetic Field: Thermodynamics

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 confiment 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.Comment: 7 pages REVTEX and 8 postscript figures, accepted in Phys. Rev.

Comment on: rotational properties of trapped bosons

Based on the Hellman-Feynman theorem it is shown that the average square radius of a cloud of interacting bosons in a parabolic well can be derived from their free energy. As an application, the temperature dependence of the moment of inertia of non-interacting bosons in a parabolic trap is determined as a function of the number of bosons. Well below the critical condensation temperature, the Bose-Einstein statistics are found to substantially reduce the moment of inertia of this system, as compared to a gas of ``distinguishable'' particles in a parabolic well.Comment: Herewith we repost our paper cond-mat/9611090 (1996). It was published in Phys. Rev. A 55, 2453 (March 1997), three years before cond-mat/0003471 (2000) by Schneider and Wallis. Reposted by [email protected]

The center-of-mass response of confined systems

For confined systems of identical particles, either bosons or fermions, we argue that the parabolic nature of the confinement potential is a prerequisite for the non-dissipative character of the center of mass response to a uniform probe. For an excitation in a parabolic confining potential, the half width of the density response function depends nevertheless quantitatively on properties of the internal degrees of freedom, as is illustrated here for an ideal confined gas of identical particles with harmonic interparticle interactions.Comment: 4 pages REVTEX; accepted as Brief Communication in Phys. Rev.