Exact spatial density of ideal Bose atoms in a two-dimensional isotropic harmonic trap. (11th January 2018)

• Record Type: Journal Article
• Authors: Cheng, Ze
• Is Part Of: Journal of statistical mechanics. (2018:Jan.)
• Publication Date: 2018-01-11
• Subjects: 1 -- 3; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa9f4b
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We have proposed an exact analytical solution to the problem of Bose–Einstein condensation (BEC) of harmonically trapped, two-dimensional (2D), and ideal atoms. It is found that the number of atoms in vapor is characterized by an analytical function, which involves a series expansion of q -digamma functions in mathematics. We employ the analytical solution to calculate the spatial density n ( r ; T, N ) of ideal Bose atoms in a 2D isotropic harmonic trap. The first main finding in this paper is that when Bose atoms are in the normal state, the density profile exhibits a 2D dark spot in the center and a bright ring outside. The second main finding is that when Bose atoms are in the BEC state, the density profile exhibits a 2D sharp peak with an extremely small radius. The third main finding is that the central density is a monotonically increasing function of the number of atoms N, but is a monotonically decreasing function of temperature T . The fourth main finding is that the number density of atoms of condensate exhibits a 2D Gaussian distribution in the center while the number density of atoms of vapor exhibits a 2D bright annulus with zero density at the origin.