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The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can…
We investigate the flow of a one-dimensional nonlinear Schrodinger model with periodic boundary conditions past an obstacle, motivated by recent experiments with Bose--Einstein condensates in ring traps. Above certain rotation velocities,…
The dynamics of a phase-separated two-component Bose-Einstein condensate are investigated, in which a bubble of one component moves through the other component. Numerical simulations of the Gross--Pitaevskii equation reveal a variety of…
The dynamical instability of weakly interacting two-component Bose--Einstein condensates with coaxial quantized vortices is analytically investigated in a two-dimensional isotopic harmonic potential. We examine whether complex eigenvalues…
We study a set of $L$ spatial bosonic modes localized on a graph $\Gamma.$ The particles are allowed to tunnel from vertex to vertex by hopping along the edges of $\Gamma.$ We analyze how, in the exact many-body eigenstates of the system…
We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate set into rotation. We consider the case of segregation of the components in the Thomas-Fermi regime, where a small parameter $\epsilon$…
We study the collisional dynamics of multiple dark solitons in a Bose-Einstein condensate confined by a toroidal trap. We assume a tight enough confinement in the radial direction to prevent possible dissipative effects due to the presence…
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability…
In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between atoms. The models are based on systems of…
We study the precessing motion of a vortex in a Bose-Einstein condensate of atomic gases. In addition to the former zero-temperature studies, finite temperature systems are treated within the Popov and semiclassical approximations.…
We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs…
We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an…
Vortex lattices in rapidly rotating Bose--Einstein condensates are systems of topological excitations that arrange themselves into periodic patterns. Here we show how phase-imprinting techniques can be used to create a controllable number…
Multiply quantized vortices in trapped Bose-Einstein condensates are studied using the Bogoliubov theory. Suitable combinations of a localized pinning potential and external rotation of the system are found to energetically stabilize, both…
Evading the Mermin-Wagner-Hohenberg no-go theorem and revisiting with rigor the ideal Bose gas confined in a square box, we explore a discrete phase transition in two spatial dimensions. Through both analytic and numerical methods we verify…
We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference…
The tippedisk is a mathematical-mechanical archetype for a peculiar friction-induced instability phenomenon leading to the inversion of an unbalanced spinning disk, being reminiscent to (but different from) the well-known inversion of the…
The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterium…