Analytic Studies of Bose-Einstein Condensation in Harmonic Traps

Yu-Ren Shi, 王雪玲, 王光辉 +3 more

罗运文, 陈继胜

In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional(1D) and quasi-two-dimensional(2D) Bose–Einstein condensation(BEC) in harmonic potential trap. The energy spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 2D Bose-Einstein condensation in harmonic potential trap is smaller.

Siegfried Großmann, Martin Holthaus

Hårek Haugerud, Tor Haugset, F. Ravndal

Luo Yun-wen, Jisheng Chen

In this paper, we investigate excited characteristic of the weakly interacting quasi-one-dimensional (1D) and quasi-two-dimensional (2D) Bose—Einstein condensation (BEC) in harmonic potential trap. The energy spectrum and the analytical expression of the sound velocity are obtained and analyzed. Compared with 3-Dimensional homogeneous Bose-condensed gas occasion, the sound velocity of 2D Bose-Einstein condensation in harmonic potential trap is smaller.

Ze Cheng

Within the framework of quantum statistical mechanics, we have proposed an analytical solution to the problem of Bose–Einstein condensation (BEC) in harmonically trapped, one-dimensional and ideal atoms. It is found that the number of atoms of vapor is characterized by an analytical function, which involves a q -digamma function in mathematics. The results of the numerical calculation of the analytical solution agree completely with the previous experimental results in the BEC of harmonically trapped, one-dimensional and ideal atoms. The analytical expressions of the critical temperature and the condensate fraction are derived in the thermodynamic limit.