The Saddle-Point Method for Condensed Bose Gases

Martin Holthaus, Eva Kalinowski

When treating the ground-state contribution exactly, a variant of the saddle-point method emerges that works even for condensed Bose gases. Results thus obtained, such as canonical partition functions, differ by universal renormalization factors from those provided by the conventional but incorrect scheme. The amended method yields the statistical properties of ideal and very weakly interacting Bose gases with a fixed number of particles with particular simplicity.

Shingo Otsuka

Siegfried Großmann, Martin Holthaus

We develop a reliable procedure for calculating the microcanonical fluctuations of the ground state occupation number for harmonically trapped ideal Bose gases, and show that these fluctuations vanish uniformly when the temperature approaches zero. The key point is the precise determination of the number of microstates from the canonical partition sum, thus avoiding a failure of the usual saddle point method. We also demonstrate why the magnitude of the condensate fluctuations does not depend on the total particle number.

晋吾 大塚

Mariusz Gajda, Kazimierz Rza̧żewski

We study the ground state occupation number and its fluctuations for the Bose-Einstein condensate of trapped atoms using the microcanonical ensemble. The analytic formulas are obtained with the help of the saddle point method. We show that microcanonical fluctuations below the critical temperature tend to zero and scale with the number of particles as $1/\sqrt{N}$.

C. J. Pethick, H. Smith