2006/06/30 by Michele Correggi, M. Correggi, Tanja Rindler-Daller +3
Mathematics · Physics and Astronomy · #Anharmonicity #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Coupling constant #Ground state #Mechanics #Physics #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #RADIUS #Strong Light-Matter Interactions #Superconductivity #Vortex #Vortex state #cond-mat.stat-mech #math-ph #math.MP #msc:35Q55 #msc:47J30 #msc:76M23
paper · pdf · doi:10.1063/1.2712421
published as J. Math. Phys. 48, 042104 (2007) · LaTex2e, 28 pages, revised version to be published in Journal of Mathematical Physics
arxiv created 2007/02/06 · openalex publication_date 2007/04/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 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)=Ω0∕ε a “hole” (i.e., a region where the density becomes exponentially small as 1∕ε→∞) develops for Ω0 above a certain critical value. If Ω(ε)⪢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 analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const∣logε∣<Ω(ε)≲const∕ε.