Exact analytical study of ideal Bose atoms in a one-dimensional harmonic trap. (16th September 2015)

• Record Type: Journal Article
• Authors: Cheng, Ze
• Is Part Of: Journal of statistical mechanics. (2015:Sep.)
• Publication Date: 2015-09-16
• Subjects: 1 -- 3; 1/110 -- 3/020; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/09/P09011
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: 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.