Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-11-18
Physics
Condensed Matter
Statistical Mechanics
39 pages of Revtex. 1 figure
Scientific paper
10.1088/0953-4075/33/19/303
In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with higher order cubic and quartic terms. The quadratic part is diagonalized exactly by transforming to a quasiparticle basis, while the non-quadratic terms are dealt with using first and second order perturbation theory. The conventional treatment of these terms, based on factorization approximations, is shown to be inconsistent. Infra-red divergences can appear in individual terms of the perturbation expansion, but we show analytically that the total contribution beyond quadratic order is finite. The resulting excitation spectrum is gapless and the energy shifts are small for a dilute gas away from the critical region, justifying the use of perturbation theory. Ultra-violet divergences can appear if a contact potential is used to describe particle interactions. We show that the use of this potential as an approximation to the two-body T-matrix leads naturally to a high-energy renormalization. The theory developed in this paper is therefore well-defined at both low and high energy and provides a systematic description of Bose-Einstein condensation in dilute gases. It can therefore be used to calculate the energies and decay rates of the excitations of the system at temperatures approaching the phase transition.
No associations
LandOfFree
A Gapless Theory of Bose-Einstein Condensation in Dilute Gases at Finite Temperature does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Gapless Theory of Bose-Einstein Condensation in Dilute Gases at Finite Temperature, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Gapless Theory of Bose-Einstein Condensation in Dilute Gases at Finite Temperature will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-567297