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Open AccessArticle

Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance

by Ofir E. Alon 1,2
1
Department of Mathematics, University of Haifa, Haifa 3498838, Israel
2
Haifa Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
Symmetry 2019, 11(11), 1344; https://doi.org/10.3390/sym11111344
Received: 30 September 2019 / Revised: 24 October 2019 / Accepted: 27 October 2019 / Published: 1 November 2019
(This article belongs to the Special Issue Symmetry and Mesoscopic Physics)
We analyze, analytically and numerically, the position, momentum, and in particular the angular-momentum variance of a Bose–Einstein condensate (BEC) trapped in a two-dimensional anisotropic trap for static and dynamic scenarios. Explicitly, we study the ground state of the anisotropic harmonic-interaction model in two spatial dimensions analytically and the out-of-equilibrium dynamics of repulsive bosons in tilted two-dimensional annuli numerically accurately by using the multiconfigurational time-dependent Hartree for bosons method. The differences between the variances at the mean-field level, which are attributed to the shape of the BEC, and the variances at the many-body level, which incorporate depletion, are used to characterize position, momentum, and angular-momentum correlations in the BEC for finite systems and at the limit of an infinite number of particles where the bosons are 100 % condensed. Finally, we also explore inter-connections between the variances. View Full-Text
Keywords: Bose–Einstein condensates; density; position variance; momentum variance; angular-momentum variance; harmonic-interaction model; MCTDHB Bose–Einstein condensates; density; position variance; momentum variance; angular-momentum variance; harmonic-interaction model; MCTDHB
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Alon, O.E. Analysis of a Trapped Bose–Einstein Condensate in Terms of Position, Momentum, and Angular-Momentum Variance. Symmetry 2019, 11, 1344.

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