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Physical Review A

Phase transition of interacting Bose gases in general power-law potentials

O. Zobay, Georgios Metikas, G. Alber

Published Jun 23, 2004• 16 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.69.063615

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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.
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We study the condensation of a homogeneous interacting Bose gas in the presence of a superimposed weak periodic potential. In contrast to, e.g., a harmonic trap, the periodic potential does not reduce the significance of long-wavelength fluctuations and thus influences the phase transition in a more profound way. We present general thermodynamic descriptions of the system above condensation in terms of mean-field as well as renormalization-group theory. Our approaches are based on describing the interplay between the effects of the interactions and the potential by means of a renormalization of the potential amplitude. These theories are then used to study the critical chemical potential and particle density and their dependence on the properties of the applied potential. A main result of our investigations concerns the characteristic nonperturbative momentum scale kc{k}_{c}kc​ of the critical interacting Bose gas. It is shown that the existence of this momentum scale becomes macroscopically manifest in the behavior of the critical thermodynamic properties.