Phase transition of interacting Bose gases in general power-law potentials (10 pages)

Georgios Metikas

O. Zobay, Georgios Metikas, G. Alber

We investigate the phase transition of interacting Bose gases in general power-law traps in the thermodynamic limit. Using energy-shell renormalization and the $\ensuremath{\epsilon}$ expansion, we evaluate the partition function for the uncondensed gas phase within a renormalization-group framework. This approach allows a unified description of homogeneous as well as inhomogeneous and anisotropic systems. Results for the critical temperature are compared to mean-field theory as well as to a local-density approximation based on renormalization-group theory for the homogeneous Bose gas. This comparison indicates the consistency of our approach. We also make suggestions for an optimized trap design in experiments that measure the transition temperature.

Giuseppe Iadonisi, M. Marinaro, Ramabhadra Vasudevan

Evgeny Levich, Victor Yakhot

O. Zobay

We review some recent theoretical work on the phase transition of interacting Bose gases in the presence of external trapping potentials. A general framework for the study of such questions is presented which is based on the application of perturbative momentum-shell renormalization group methods to the trapped gas in the uncondensed phase. After giving an overview of this approach, we first establish its validity by comparing to previous results for homogeneous and harmonically trapped gases. Using this theoretical framework, we then examine various aspects of how external potentials influence the physics of condensation. (i) By studying the case of general power-law potentials and complemented by arguments from variational perturbation theory, it is quantitatively worked out how a growing inhomogeneity of the trapping potential diminishes nonperturbative effects at the transition. (ii) It is shown how by superimposing a weak periodic potentials on the homogeneous system, the characteristic nonperturbative momentum scale of critical interacting Bose gases can be probed. (iii) For a gas in a random potential, it is studied how condensation is affected by the combined influence of disorder effects and particle interactions.

B. Ya. Balagurov, Валентин Григорьевич Вакс