Exact analytical study of ideal Bose atoms in a two-dimensional isotropic harmonic trap. (15th June 2017)

• Record Type: Journal Article
• Authors: Cheng, Ze
• Is Part Of: Journal of statistical mechanics. (2017:Jun.)
• Publication Date: 2017-06-15
• Subjects: 1 -- 3; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa727b
• 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) of harmonically trapped, two-dimensional, and ideal atoms. It is found that the number of atoms in vapor is characterized by an analytical function, which involves a series of q -digamma functions in mathematics. The results of numerical calculation of the analytical solution agree completely with the foregoing experimental results in the BEC of harmonically trapped, two-dimensional, and ideal atoms. The analytical expressions of the critical temperature and the condensate fraction are derived in the thermodynamic limit. It is found that the two-dimensional critical temperature is smaller than the one-dimensional critical temperature by an order of magnitude or more.