Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1410.5006 · The European Physical Journal D

Comparison between the numerical solutions and the Thomas-Fermi approximation for atomic-molecular Bose-Einstein condensates

Leonardo S. F. Santos, Marcelo O. C. Pires, Davi Giugno

Published Feb 27, 2015• 0 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2015-50863-7

Related papers

A numerical study of the ground state and dynamics of atomic–molecular Bose–Einstein condensates

Wei Jiang, Hanquan Wang, Xiang‐Gui Li

Computer Physics Communications•Jun 10, 2013•4 citations

Formation of vortices in a dense Bose-Einstein condensate

Vicente Pereira de Barros, Ch. Moseley, A. Gammal +1 more

A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond the Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized nonlinear Schr\"odinger equation with a kinetic term for the rotating condensate. In comparison with previous calculations, based on the Thomas-Fermi approximation, significant improvements are found in regions where the condensate in a trap potential is not smooth. The critical angular velocity of the vortex formation is higher than in the Thomas-Fermi prediction.

arXiv:0806.4106•Physical Review A•Jul 31, 2008•2 citations

Semi-Analytic Ground State Solutions of Two-Component Bose-Einstein Condensate in Two Dimensions

Swati Sridhar

In this thesis we study a two-component Bose-Einstein Condensate system in 2D, using a combination of approximate analytical and exact numerical methods of solving the Gross-Pitaevskii equation (GPE). We discuss some of the ways of finding approximate ground state solutions to the GPE, one of them being the Thomas-Fermi approximation. Using the Thomas-Fermi approximation, one can separate the system into two regimes; one where both components are disks and one where one of the components is a disk and the other component is an annulus. However, the Thomas-Fermi approximation does not hold true beyond a critical value. We demonstrate a method using which one can get more precise solutions for the GPE. This involves using a method of approximation of the GPE near the critical boundaries, which has been previously used for a single component Bose gas. This can be adapted for a two-component system in order obtain explicit solutions for a BEC in a 2D harmonic trap with repulsive interactions. We show in detail how this approximation works for the different regimes suggested by the Thomas-Fermi analysis and also for more generalized cases where one has different masses, particle numbers and trapping frequencies for the two components. This thesis also talks about how one could analyse the system using this approximation in 1D and 3D, shedding more light on what might be the parameters affecting the precision of the solution.

•Jan 1, 2014•0 citations

Modeling the Expansion of Bose--Einstein Condensate Mixtures in the Thomas--Fermi Limit

Alison Lota, Laura Halmo, Charles Holcombe +1 more

Bulletin of the American Physical Society•Mar 8, 2007•0 citations

Numerical analysis of transition temperature in Bose–Einstein condensation

Shoichi Sakamoto, 茂人 市野, Hideki Matsumoto

Physica B Condensed Matter•May 1, 2003•0 citations

Time Evolution of Freely Expanded Bose-Einstein Condensates Containing Small Numbers of Atoms

De-Sheng Hong, K. H. Huang, Tsin-Fu Jiang +1 more

We investigate the time evolution of freely expanded Bose-Einstein condensates by measuring their aspect ratios at different times after their release from a magnetic trap. In these measurements the condensates contain no more than 9000 87Rb atoms. By varying the trapping frequency and atom number, we measure the condensate aspect ratios at different expansion times in free space. We compare our measurements with those calculated from the Thomas-Fermi model and a direct numerical solution. Under our trapping condition, the data of the time dependent aspect ratios of the freely expanded condensates reasonably agrees with the numerical calculations, but shows a clear deviation from the predictions of the Thomas-Fermi model when the atom number in the condensates is small.

Chinese Journal of Physics•Apr 1, 2007•0 citations
A relaxation method is employed to study a rotating dense Bose-Einstein condensate beyond the Thomas-Fermi approximation. We use a slave-boson model to describe the strongly interacting condensate and derive a generalized nonlinear Schr\"odinger equation with a kinetic term for the rotating condensate. In comparison with previous calculations, based on the Thomas-Fermi approximation, significant improvements are found in regions where the condensate in a trap potential is not smooth. The critical angular velocity of the vortex formation is higher than in the Thomas-Fermi prediction.
In this thesis we study a two-component Bose-Einstein Condensate system in 2D, using a combination of approximate analytical and exact numerical methods of solving the Gross-Pitaevskii equation (GPE). We discuss some of the ways of finding approximate ground state solutions to the GPE, one of them being the Thomas-Fermi approximation. Using the Thomas-Fermi approximation, one can separate the system into two regimes; one where both components are disks and one where one of the components is a disk and the other component is an annulus. However, the Thomas-Fermi approximation does not hold true beyond a critical value. We demonstrate a method using which one can get more precise solutions for the GPE. This involves using a method of approximation of the GPE near the critical boundaries, which has been previously used for a single component Bose gas. This can be adapted for a two-component system in order obtain explicit solutions for a BEC in a 2D harmonic trap with repulsive interactions. We show in detail how this approximation works for the different regimes suggested by the Thomas-Fermi analysis and also for more generalized cases where one has different masses, particle numbers and trapping frequencies for the two components. This thesis also talks about how one could analyse the system using this approximation in 1D and 3D, shedding more light on what might be the parameters affecting the precision of the solution.
We investigate the time evolution of freely expanded Bose-Einstein condensates by measuring their aspect ratios at different times after their release from a magnetic trap. In these measurements the condensates contain no more than 9000 87Rb atoms. By varying the trapping frequency and atom number, we measure the condensate aspect ratios at different expansion times in free space. We compare our measurements with those calculated from the Thomas-Fermi model and a direct numerical solution. Under our trapping condition, the data of the time dependent aspect ratios of the freely expanded condensates reasonably agrees with the numerical calculations, but shows a clear deviation from the predictions of the Thomas-Fermi model when the atom number in the condensates is small.