Thermodynamics of a weakly interacting Bose-Einstein gas

Abstract

The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the standard ground state energy and pressureas function of the particle density. At finite temperatures it is found necessary to include ring corrections to the one-loop result in order to satisfy the Goldstone theorem. It is natural to introduce an effective chemical potential directly related to the order parameter and which uniformly decreases with increasing temperatures. This is in contrast to the the ordinary chemical potential which peaks at the critical temperature. The resulting thermodynamics in the condensed phase at very low temperatures is found to be the same as in the Bogoliubov approximation where the degrees of freedom are given by the Goldstone bosons. At higher temperatures the ring corrections dominate and result in a critical temperature unaffected by the interaction.

39 pages, 9 figures, picTex, submitted to Annals of Physics. Discussions on renormalization and off-diagonal self energies are made clearer in this version. A short derivation of the non-relativistic limit is added

Cited by in corpus (19)

• Theory of the Weakly Interacting Bose Gas
• Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature
• Dependence of the BEC transition temperature on interaction strength: a perturbative analysis
• U(1)-Symmetry breaking and violation of axial symmetry in TlCuCl3 and other insulating spin systems
• Thermal field theory of bosonic gases with finite-range effective interaction
• Bose - Einstein condensation of triplons with a weakly broken U(1) symmetry
• Gr{ü}neisen parameter of quantum magnets with spin gap
• The Effective Single-mode model of a Binary Boson Mixture in the Quantum Droplet Region
• Effective Potential and Thermodynamics for a Coupled Two-Field Bose Gas Model
• Semiclassical Corrections to a Static Bose-Einstein Condensate at Zero Temperature
• Symmetry Aspects in Nonrelativistic Multi-Scalar Field Models and Application to a Coupled Two-Species Dilute Bose Gas
• zeta-function regularization and the interacting Bose gas at low temperature
• Nonuniversal Equation of State of a Quasi-2D Bose Gas in Dimensional Crossover
• Thermodynamics of a weakly interacting Bose gas above the transition temperature
• Effective field theory of bosons with finite-range interaction in a disordered environment
• Transition temperature and thermodynamic properties of homogeneous weakly interacting Bose gas in self-consistent Popov approximation
• Cornwall-Jackiw-Tomboulis effective field theory to nonuniversal equation of state of an ultracold Bose gas
• Hugenholtz -- Pines relations and the critical temperature of a Rabi coupled binary Bose system
• Bogoliubov phonons in a Bose-Einstein condensate from the one-loop perturbative renormalization group