240 research outputs found
A Tale of Two Distributions: From Few To Many Vortices In Quasi-Two-Dimensional Bose-Einstein Condensates
Motivated by the recent successes of particle models in capturing the
precession and interactions of vortex structures in quasi-two-dimensional
Bose-Einstein condensates, we revisit the relevant systems of ordinary
differential equations. We consider the number of vortices as a parameter
and explore the prototypical configurations ("ground states") that arise in the
case of few or many vortices. In the case of few vortices, we modify the
classical result of Havelock [Phil. Mag. , 617 (1931)] illustrating
that vortex polygons in the form of a ring are unstable for .
Additionally, we reconcile this modification with the recent identification of
symmetry breaking bifurcations for the cases of . We also briefly
discuss the case of a ring of vortices surrounding a central vortex (so-called
configuration). We finally examine the opposite limit of large and
illustrate how a coarse-graining, continuum approach enables the accurate
identification of the radial distribution of vortices in that limit.Comment: 15 pages, 2 figure
An Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments
Assume a lower-dimensional solitonic structure embedded in a higher
dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark
soliton in 2D space, a spherical shell soliton in 3D space etc. By extending
the Landau dynamics approach [Phys. Rev. Lett. {\bf 93}, 240403 (2004)], we
show that it is possible to capture the transverse dynamical modes (the "Kelvin
modes") of the undulation of this "soliton filament" within the higher
dimensional space. These are the transverse stability/instability modes and are
the ones potentially responsible for the breakup of the soliton into structures
such as vortices, vortex rings etc. We present the theory and case examples in
2D and 3D, corroborating the results by numerical stability and dynamical
computations.Comment: 5 pages, 3 figure
Three-Dimensional Nonlinear Lattices: From Oblique Vortices and Octupoles to Discrete Diamonds and Vortex Cubes
We construct a variety of novel localized states with distinct topological
structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states
can be created in Bose-Einstein condensates trapped in strong optical lattices,
and crystals built of microresonators. These new structures, most of which have
no counterparts in lower dimensions, range from purely real patterns of dipole,
quadrupole and octupole types to vortex solutions, such as "diagonal" and
"oblique" vortices, with axes oriented along the respective directions
and . Vortex "cubes" (stacks of two quasi-planar vortices
with like or opposite polarities) and "diamonds" (discrete skyrmions formed by
two vortices with orthogonal axes) are constructed too. We identify stability
regions of these 3D solutions and compare them with their 2D counterparts, if
any. An explanation for the stability/instability of most solutions is
proposed. The evolution of unstable states is studied as well.Comment: 4 pages, 4 figures, submitted January 200
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