Self-Similar Approximations for a Trapped Bose-Einstein Condensate
V. I. Yukalov, E. P. Yukalova, and V. S. Bagnato
TL;DR
This paper introduces a self-similar approximation method to solve the Gross-Pitaevskii equation for Bose-Einstein condensates in spherical traps, providing accurate interpolations across all coupling strengths.
Contribution
It presents a novel self-similar approximation approach that improves accuracy over existing methods for modeling Bose-Einstein condensates in harmonic traps.
Findings
More accurate than Gaussian and Thomas-Fermi approximations
Valid across entire coupling parameter range
Applicable to nonspherical traps
Abstract
An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling and strong-coupling limits. This solution is shown to be more accurate than the optimized Gaussian approximation as well as the Thomas-Fermi approximation. The derivation of the solution is based on the self-similar approximation theory. The possibility of obtaining interpolation formulas in the case of nonspherical traps is discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.