Abstract
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.
Highlights
Bose–Einstein condensates (BECs) made of ultra-cold atoms offer a wide platform to study many-body physics [1,2,3,4,5]
The energy per particle, density per particle, and reduced density matrices [17] per particle computed at the many-body level of theory boil down to those obtained in mean-field theory [7,8,9,10,14,16], despite the fact that the respective many-boson wavefunctions are different [13,15]
In the present work we study, analytically and numerically, the angular-momentum variance of a trapped BEC in a two-dimensional anisotropic trap for static and dynamic scenarios, and analyze the difference between the many-body and mean-field variances for finite systems and at the limit of an infinite number of particles
Summary
Bose–Einstein condensates (BECs) made of ultra-cold atoms offer a wide platform to study many-body physics [1,2,3,4,5]. The first examples [11,12] concentrated on one-dimensional problems and the position and momentum variances, and investigated conditions and mechanisms for the differences between the respective many-body and mean-field variances at the particle limit. Symmetry (in terms of its conservation) than the many-body angular-momentum variance are identified Going beyond these works, in the present work we study, analytically and numerically, the angular-momentum variance of a trapped BEC in a two-dimensional anisotropic trap for static and dynamic scenarios, and analyze the difference between the many-body and mean-field variances for finite systems and at the limit of an infinite number of particles. We study the respective position and momentum variances, and thereby offer a comprehensive characterization of the BEC in terms of its variances This would allow us to put forward inter-connections between the variances. Appendix A discusses translations of variances and inter-connections of the latter
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