Thermodynamics of a trapped interacting Bose gas and the renormalization group

TL;DR

This paper uses renormalization group theory to analyze a trapped interacting Bose gas, deriving flow equations and studying the transition temperature's dependence on scattering length, with results aligning with prior research.

Contribution

It extends renormalization group analysis to trapped Bose gases, deriving flow equations and connecting them to homogeneous systems, providing insights into transition temperature behavior.

Findings

Flow equations for trapped Bose gas derived

Transition temperature dependence on scattering length analyzed

Results agree with previous studies

Abstract

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 Wilsonian energy-shell renormalization and the 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 results to study the transition temperature as a function of the scattering length. Our results compare well to previous studies of the problem.