Renormalization Group Analysis of a Confined, Interacting Bose Gas

The renormalization group is not only a powerful method for describing universal properties of phase transitions but it is also useful for evaluating non- universal properties beyond mean-field theory. In this contribution we concentrate on these latter aspects of the renormalization group approach. We introduce its main underlying ideas in the familiar context of the ideal Bose gas and then apply them to the case of an interacting, confined Bose gas within the framework of the random phase approximation. We model confinement by periodic boundary conditions and demonstrate how confinement modifies the flow equations of the renormalization group changing thus the thermodynamic properties of the gas.