Exact breather solutions of repulsive Bose atoms in a one-dimensional harmonic trap

Ze Cheng ()
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Ze Cheng: School of Physics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

International Journal of Modern Physics C (IJMPC), 2018, vol. 29, issue 10, 1-14

Abstract: Bose–Einstein condensates of repulsive Bose atoms in a one-dimensional harmonic trap are investigated within the framework of a mean field theory. We solve the one-dimensional nonlinear Gross–Pitaevskii (GP) equation that describes atomic Bose–Einstein condensates. As a result, we acquire a family of exact breather solutions of the GP equation. We numerically calculate the number density n(z,t,N) of atoms that is associated with these solutions. The first discovery of the calculation is that at the instant of the saddle point, the density profile exhibits a sharp peak with extremely narrow width. The second discovery of the calculation is that in the center of the trap (z=0 m), the number density is a U-shaped function of the time t. The third discovery of the calculation is that the surface plot of the density n(z,t) likes a saddle surface. The fourth discovery of the calculation is that as the number N of atoms increases, the Bose–Einstein condensate in a one-dimensional harmonic trap becomes stabler and stabler.

Keywords: Bose–Einstein condensate; one-dimensional trap; nonlinear Gross–Pitaevskii equation; exact breather solutions (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S0129183118501000

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