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.

Density and Pair Correlation Function of Confined Identical Particles: the Bose-Einstein Case

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.Comment: 8 pages (REVTEX) + 6 figures (postscript

Momentum distribution of confined bosons: temperature dependence

The momentum distribution function of a parabolically confined gas of bosons with harmonic interparticle interactions is derived. In the Bose-Einstein condensation region, this momentum distribution substantially deviates from a Maxwell-Boltzmann distribution. It is argued that the determination of the temperature of the boson gas from the Bose-Einstein momentum distribution function is more appropriate than the currently used fitting to the high momentum tail of the Maxwell-Boltzmann distribution.Comment: 5 REVTEX pages + 2 postscript figures. Accepted in Phys. Rev.

Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions

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.Comment: 11 REVTEX pages, 3 postscript figures. Accepted for publication in Phys. Rev. E, Vol. 58 (August 1, 1998

Density of a gas of spin polarized fermions in a magnetic field

For a fermion gas with equally spaced energy levels that is subjected to a magnetic field, the particle density is calculated. The derivation is based on the path integral approach for identical particles, in combination with the inversion techniques for the generating function of the static response functions. Explicit results are presented for the ground state density as a function of the magnetic field with a number of particles ranging from 1 to 45.Comment: 9 pages, 8 figures; To appear in Phys. Rev. E on December 1, 2000; e-mail addresses: [email protected], [email protected], [email protected], [email protected]

Observations on the Helminths of Harbour Porpoises (Phocoena Phocoena) and Common Guillemots (Uria Aalge) from the Belgian and German Coasts

Between February 1990 and July 1991, 18 harbour porpoises (Phocoena phocoena) and 248 common guillemots (Uria aalge), found dead along the Belgian and German coasts, were examined for their burden of helminths. A total of three species were found in the guillemots (one cestode, one nematode and one pentastomid), and six species in the porpoises (one trematode, one cestode and four nematodes). Among the guillemots the burden of helminths was not statistically different between juvenile and adult birds. The deaths of the birds were apparently not related to the parasite infections. In contrast, the adult porpoises were more heavily parasitised than the juveniles, except for one young porpoise stranded on the Belgian coast. In the porpoises, four species of parasites had a pathological effect and Torynurus convolutus was responsible for the death of one animal from the Belgian coast and three from the German coast

Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism

A generalization of symmetrized density matrices in combination with the technique of generating functions allows 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 payed to the thermodynamic properties of bosons and their condensation.Comment: 13 REVTEX pages + 9 postscript figure

Pathological investigations on guillemots (Uria aalge) stranded on the Belgian coast during the winter of 1993-94

peer reviewedPathological investigations were carried out on 67 guillemots (Uria aalge) washed up on the Belgian coast between November 1993 and March 1994. Emaciation and acute haemorrhagic gastroenteropathy were observed in more than 70 per cent of the birds. There was no statistical relationship between the level of oil contamination and the severity of the lesions. Differences in bodyweight were accounted for by age, sex, emaciation, and acute haemorrhagic gastroenteropathy. The birds had a severe weight deficit but the concentrations of pollutants were below acutely toxic levels

Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations

Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation of the partition functions for particles that carry internal quantum numbers. The partition function is shown to be a sum of one or more group characters. The utility of character expansions in calculating the partition functions is explored. Several examples are given to illustrate these techniques.Comment: 16 pages of RevTe

Condensation and interaction range in harmonic boson traps: a variational approach

For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric representation. Within the harmonic approximation a variational estimate of the effect of the interaction range on the existence of many-particle bound states, and on the N-T phase diagram is obtained.Comment: 14 pages+4 figures, submitted to phys.rev.