Stability and instability properties of rotating Bose-Einstein condensates

Abstract

We consider the mean-field dynamics of Bose-Einstein condensates in rotating harmonic traps and establish several stability and instability properties for the corresponding solution. We particularly emphasize the difference between the situation in which the trap is symmetric with respect to the rotation axis and the one where this is not the case.

13 pages; corrected a systematic typo

References in corpus (11)

• Rapidly Rotating Atomic Gases
• Bosons in anisotropic traps: ground state and vortices
• Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional
• Vortices in attractive Bose-Einstein condensates in two dimensions
• Gross-Pitaevskii Theory of the Rotating Bose Gas
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• Ground State Asymptotics of a Dilute, Rotating Gas
• Split-merge cycle, fragmented collapse, and vortex disintegration in rotating Bose-Einstein condensates with attractive interactions
• Center of mass rotation and vortices in an attractive Bose gas
• Gravity-induced resonances in a rotating trap
• Bifurcations of multi-vortex configurations in rotating Bose--Einstein condensates

Cited by in corpus (10)

• The Nonexistence of Vortices for Rotating Bose-Einstein Condensates with Attractive Interactions
• Growth of Sobolev norms for coupled Lowest Landau Level equations
• Local Uniqueness of Ground States for Rotating Bose-Einstein Condensates with Attractive Interactions
• Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation
• The Nonexistence of Vortices for Rotating Bose-Einstein Condensates in Non-Radially Symmetric Traps
• Computing the action ground state for the rotating nonlinear Schrödinger equation
• On stability of rotational 2D binary Bose-Einstein condensates
• Multiplicity, asymptotics and stability of standing waves for nonlinear Schrödinger equation with rotation
• On action ground states of defocusing nonlinear Schrödinger equations
• Enhancement of the Zakharov-Glassey's method for Blow-Up in nonlinear Schroedinger equations