Related papers: Stability of self-gravitating Bose-Einstein-Conden…
We study the ground state which minimizes a Gross-Pitaevskii energy with general non-radial trapping potential, under the unit mass constraint, in the Thomas-Fermi limit where a small parameter tends to 0. This ground state plays an…
We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii…
The stability of a Bose-Einstein condensed state of trapped ultra-cold atoms is investigated under the assumption of an attractive two-body and a repulsive three-body interaction. The Ginzburg-Pitaevskii-Gross (GPG) nonlinear Schr\"odinger…
We systematically construct stationary soliton states in a one-component, two-dimensional, repulsive, Gross-Pitaevskii equation with a ring-shaped target-like trap similar to the potential used to confine a Bose-Einstein condensate in a…
Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson…
We analyze the ground state of a Bose-Einstein condensate in the presence of higher-order interaction (HOI), modeled by a modified Gross-Pitaevskii equation (MGPE). In fact, due to the appearance of HOI, the ground state structures become…
It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number…
We investigate dipolar Bose-Einstein condensates in a complex external double-well potential that features a combined parity and time-reversal symmetry. On the basis of the Gross-Pitaevskii equation we study the effects of the long-ranged…
We consider a gas of $N$ bosons in a box with volume one interacting through a two-body potential with scattering length of order $N^{-1}$ (Gross-Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently small, we show that…
The dynamics of a ring of vortices in two-dimensional Bose-Einstein condensates (with and without an additional vortex at the center) is studied for (1) a uniform condensate in a rigid cylinder and (2) a nonuniform trapped condensate in the…
The stability of colliding Bose-Einstein condensates is investigated. A set of coupled Gross-Pitaevskii equations is thus considered, and analyzed via a perturbative approach. No assumption is made on the signs (or magnitudes) of the…
We derive general approximate formulas that provide with remarkable accuracy the ground-state properties of any mean-field scalar Bose-Einstein condensate with short-range repulsive interatomic interactions, confined in arbitrary…
A condensate with two internal states coupled by external electromagnetic radiation, is described by coupled Gross Pitaevskii equations, whose eigenstates are analogous to the dressed states of quantum optics. We solve for these eigenstates…
Vortex states of weakly-interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the…
Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas…
We study theoretically a gas consisting of charged bosons (ions) over the flat dielectric surface at low temperatures and its tendency to form a state with a Bose-Einstein condensate. For the stability of a system, an additional external…
We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by $1/\eps^2$ and the…
We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding…
This paper studies the localization behaviour of Bose-Einstein condensates in disorder potentials, modeled by a Gross-Pitaevskii eigenvalue problem on a bounded interval. In the regime of weak particle interaction, we are able to quantify…
The stability of a quantized vortex state in Bose-Einstein condensation is examined within Bogoliubov theory for alkali atom gases confined in a harmonic potential under forced rotation. By solving the non-linear Bogoliubov equations…