Emergence and Stability of Vortex Clusters in Bose-Einstein Condensates: a Bifurcation Approach near the Linear Limit
arXiv:1012.1840 · doi:10.1016/j.physd.2011.06.002
Abstract
We study the existence and stability properties of clusters of alternating charge vortices in Bose-Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are identified as well.
8 pages, 7 figures
References in corpus (11)
- Spontaneous vortices in the formation of Bose-Einstein condensates
- Classical bifurcation at the transition from Rabi to Josephson dynamics
- Vortex stability in nearly two-dimensional Bose-Einstein condensates with attraction
- Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
- Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
- A vortex dipole in a trapped two-dimensional Bose-Einstein condensate
- Stability and dynamics of vortex clusters in nonrotated Bose-Einstein condensates
- Size and dynamics of vortex dipoles in dilute Bose-Einstein condensates
- Dynamics of vortices in weakly interacting Bose-Einstein condensates
- Impact of anisotropy on vortex clusters and their dynamics
- Weak-Hamiltonian dynamical systems
Cited by in corpus (16)
- Dark spherical shell solitons in three-dimensional Bose-Einstein condensates: Existence, stability and dynamics
- Vector Dark-Antidark Solitary Waves in Multi-Component Bose-Einstein condensates
- Vortex-Bright Soliton Dipoles: Bifurcations, Symmetry Breaking and Soliton Tunneling in a Vortex-Induced Double Well
- Generating Functions, Polynomials and Vortices with Alternating Signs in Bose-Einstein Condensates
- The Snake Instability of Ring Dark Solitons in Toroidally Trapped Bose-Einstein Condensates
- Computing stationary solutions of the two-dimensional Gross-Pitaevskii equation with Deflated continuation
- Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
- Dark-bright ring solitons in Bose-Einstein condensates
- Stabilization of ring dark solitons in Bose-Einstein condensates
- On the Bifurcation and Stability of Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates
- Onset of transverse instabilities of confined dark solitons
- Dynamics of vortex quadrupoles in nonrotating trapped Bose-Einstein condensate
- Few-Particle Vortex Cluster Equilibria in Bose-Einstein Condensates: Existence and Stability
- Existence, stability and nonlinear dynamics of vortices and vortex clusters in anisotropic Bose-Einstein condensates
- Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup
- Superfluid vortex multipoles and soliton stripes on a torus