The saddle-point method for condensed Bose gases

Details The saddle-point method for condensed Bose gases The saddle-point method for condensed Bose gases

1999-06-07

arxiv.org/abs/cond-mat/9906092v1

Physics

Condensed Matter

Statistical Mechanics

32 pages, 11 figures. Ann. Phys. (N.Y.), in press

Scientific paper

10.1006/aphy.1999.5950

The application of the conventional saddle-point approximation to condensed Bose gases is thwarted by the approach of the saddle-point to the ground-state singularity of the grand canonical partition function. We develop and test a variant of the saddle-point method which takes proper care of this complication, and provides accurate, flexible, and computationally efficient access to both canonical and microcanonical statistics. Remarkably, the error committed when naively employing the conventional approximation in the condensate regime turns out to be universal, that is, independent of the system's single-particle spectrum. The new scheme is able to cover all temperatures, including the critical temperature interval that marks the onset of Bose--Einstein condensation, and reveals in analytical detail how this onset leads to sharp features in gases with a fixed number of particles. In particular, within the canonical ensemble the crossover from the high-temperature asymptotics to the condensate regime occurs in an error-function-like manner; this error function reduces to a step function when the particle number becomes large. Our saddle-point formulas for occupation numbers and their fluctuations, verified by numerical calculations, clearly bring out the special role played by the ground state.

Affiliated with

Also associated with

No associations

Rating

The saddle-point method for condensed Bose gases 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 saddle-point method for condensed Bose gases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The saddle-point method for condensed Bose gases will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-707703