Interaction energy of a Bose gas in a harmonic trap

Lixuan Chen

The thermodynamic properties of a weakly interacting Bose gas trapped in a harmonic potential are studied based on the local-density approximation (LDA). The spatial distributions of particle number and energy and the expressions of some important thermodynamic quantities are derived analytically. The effects of the interatomic interaction on the thermodynamic properties of the system are discussed.

Ji-Xuan Hou, Jing Yang

Georgios Metikas, O. Zobay, G. Alber

We apply perturbative renormalization-group theory to the symmetric phase of a dilute interacting Bose gas which is trapped in a three-dimensional harmonic potential. Using Wilson's energy-shell renormalization and the $\ensuremath{\epsilon}$ expansion, we derive the flow equations for the system. We relate these equations to the flow for the homogeneous Bose gas. In the thermodynamic limit, we apply our approach to examine the transition temperature of the harmonically trapped Bose gas as a function of the scattering length. The results are compared to previous studies of the problem.

Alexander Yu. Cherny, Arkady A Shanenko

Chong Wang, Yan Ke-zhu, 曲阜师范大学物理系,曲阜 273165

In this article we study BoseEinstein condensation of the gas with interactions in a harmonic trap using a numerical method. The distribution of the energy states was given, by which the author calculated the shift of the critical temperature and made a comparison with the situation without interactions. We have obtained a positive shift of critical temperature for systems with repulsive interaction, and a negative one for systems with attractive interaction.

Gert‐Ludwig Ingold, Astrid Lambrecht