On the Third Critical Speed for Rotating Bose-Einstein Condensates

Abstract

We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevksii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in [M. Correggi {\it et al}, {\it J. Math. Phys. \textbf{53}(2012)] that such a transition occurs when the angular velocity is of order ${\epsilon }^{-4}$, with ${\epsilon }^{-2}$ denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and $\epsilon \ll 1$ (Thomas-Fermi regime). In this paper we identify a finite value ${\Omega }_{\mathrm{c}}$ such that, if $\Omega ={\Omega }_0/{\epsilon }^4$ with ${\Omega }_0>{\Omega }_{\mathrm{c}}$, the condensate is in the giant vortex phase. Under the same condition we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.

pdfLaTeX, 39 pages, minor changes, to appear in J. Math. Phys

References in corpus (12)

• Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
• Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps
• Critical Rotational Speeds for Superfluids in Homogeneous Traps
• Boundary Behavior of the Ginzburg-Landau Order Parameter in the Surface Superconductivity Regime
• On the Ginzburg--Landau Functional in the Surface Superconductivity Regime
• Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions
• Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps
• Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
• The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps
• Giant vortex phase transition in rapidly rotating trapped Bose-Einstein condensates
• Vortex Phases of Rotating Superfluids
• Energy of a rotating Bose-Einstein condensate in a harmonic trap

Cited by in corpus (4)

• The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with Attractive Interactions
• Surface Effects in Superconductors with Corners
• Effects of Corners in Surface Superconductivity
• Almost Flat Angles in Surface Superconductivity