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 $N$ 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. ${\bf 11}$, 617 (1931)] illustrating that vortex polygons in the form of a ring are unstable for $N \geq7$. Additionally, we reconcile this modification with the recent identification of symmetry breaking bifurcations for the cases of $N=2,\dots,5$. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-called $N+1$ configuration). We finally examine the opposite limit of large $N$ 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

Multiquantum well spin oscillator

A dc voltage biased II-VI semiconductor multiquantum well structure attached to normal contacts exhibits self-sustained spin-polarized current oscillations if one or more of its wells are doped with Mn. Without magnetic impurities, the only configurations appearing in these structures are stationary. Analysis and numerical solution of a nonlinear spin transport model yield the minimal number of wells (four) and the ranges of doping density and spin splitting needed to find oscillations.Comment: 11 pages, 2 figures, shortened and updated versio

Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system we are able to construct complex periodic orbits in the original, partial differential equation, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations

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