Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps

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dc.creatorCorreggi, M.
dc.creatorRindler-Daller, T.
dc.creatorYngvason, J.
dc.date2006-06-23
dc.date2007-02-06
dc.date.accessioned2026-07-07T08:14:44Z
dc.date.available2026-07-07T08:14:44Z
dc.descriptionWe study a rotating Bose-Einstein Condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as $1/ε^2$ and we are interested in the limit $ε\to 0$ (TF limit) with the angular velocity $Ω$ depending on $ε$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when $Ω$ tends to infinity as a power of $1/ε$. If $Ω(ε)=Ω_0/ε$ a ``hole'' (i.e., a region where the density becomes exponentially small as $1/ε\to\infty$) develops for $Ω_0$ above a certain critical value. If $Ω(ε)\gg 1/ε$ the hole essentially exhausts the container and a ``giant vortex'' develops with the density concentrated in a thin layer at the boundary. While we do not analyse the detailed vortex structure we prove that rotational symmetry is broken in the ground state for ${\rm const.}|\logε|<Ω(ε)\lesssim \mathrm{const.}/ε$.
dc.descriptionLaTex2e, 28 pages, revised version to be published in Journal of Mathematical Physics
dc.identifierhttps://arxiv.org/abs/math-ph/0606058
dc.identifierhttp://arxiv.org/abs/math-ph/0606058
dc.identifierJ. Math. Phys. 48, 042104 (2007)
dc.identifierdoi:10.1063/1.2712421
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133233
dc.subjectMathematical Physics
dc.subjectStatistical Mechanics
dc.subject35Q55, 47J30, 76M23
dc.titleRapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps
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