We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1 ε2 and we are interested in the limit ε→0 (Thomas-Fermi limit) with the angular velocity depending on ε. We derive rigorously the leading asymptotics of the ground state energy and the density profile when tends to infinity as a power of 1ε. If (ε) = 0 ε a "hole" (i.e., a region where the density becomes exponentially small as 1ε→∞) develops for 0 above a certain critical value. If (ε) 1ε 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 analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const ∫log ε∫ < (ε) constε. © 2007 American Institute of Physics.

Rapidly rotating Bose-Einstein condensates in strongly anharmonic traps

Correggi M.;
2007-01-01

Abstract

We study a rotating Bose-Einstein condensate in a strongly anharmonic trap (flat trap with a finite radius) in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1 ε2 and we are interested in the limit ε→0 (Thomas-Fermi limit) with the angular velocity depending on ε. We derive rigorously the leading asymptotics of the ground state energy and the density profile when tends to infinity as a power of 1ε. If (ε) = 0 ε a "hole" (i.e., a region where the density becomes exponentially small as 1ε→∞) develops for 0 above a certain critical value. If (ε) 1ε 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 analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const ∫log ε∫ < (ε) constε. © 2007 American Institute of Physics.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1134394
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