English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article we introduce a multi-modal variational method to analyticallyestimate the full number- and corresponding energy-density profile of a spin-1Bose-Einstein condensate (BEC) for a number of particles as low as 500 underharmonic confinement. To apply this method, we consider a system of spin-1 BECunder three-dimensional isotropic and effective one-dimensional harmonicconfinement in the absence (negligible presence) of the magnetic field whichhas ground state candidates of comparable energy. It should be noted that insuch circumstances kinetic energy contribution to the ground state cannot beneglected which puts the applicability of Thomas-Fermi approximation toquestion. For anti-ferromagnetic condensates, the T-F approximated energydifference between the competing stationary states (ground state and the firstexcited state) is approximately 0.3\%. As T-F approximation is only good forcondensates with a large number of particles, T-F approximated predictions cancompletely go wrong especially for small condensates. This is where comes therole of a detailed analysis using our variational method, which incorporatesthe kinetic energy contribution and accurately estimates the number- andenergy-density profile even for condensates having a small number of particles.Results of our analytical method are supported by numerical simulation. Thisvariational method is general and can be extended to othersimilar/higher-dimensional problems to get results beyond the accuracy of theThomas-Fermi approximation.

the european physical journal plus

A variational approach for the ground state profile of a trapped  spinor-BEC: A detailed study of phase transition in spin-1 condensate at zero  magnetic field