The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom

Details The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom

1999-07-16

arxiv.org/abs/cond-mat/9907241v1

Physics

Condensed Matter

Statistical Mechanics

10 pages, Revtex, submitted to Europhysics Letters

Scientific paper

10.1209/epl/i2000-00130-3

We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $\delta T_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.

Affiliated with

Also associated with

No associations

Rating

The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom 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 The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-162597