相关论文: The Nonexistence of Vortices for Rotating Bose-Ein…
We study ground states of two-dimensional Bose-Einstein condensates with repulsive ($a>0$) or attractive ($a<0$) interactions in a trap $V (x)$ rotating at the velocity $\Omega $. It is known that there exist critical parameters $a^*>0$ and…
We consider ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps $V(x)=x_1^2+\Lambda ^2x_2^2 $, where $0<\Lambda \not =1$ and $x=(x_1, x_2)\in R^2$. For any fixed rotational…
We study minimizers of a Gross--Pitaevskii energy describing a two-component Bose-Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of coexistence of the components in the…
We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap $V(x)$ rotating at the velocity $\Omega $. It is known that there exist a critical rotational velocity $0<\Omega ^*:=\Omega^*(V)\leq…
We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our…
This paper is concerned with ground states of two-component Bose gases confined in a harmonic trap $V(x)=x_1^2+\Lambda^2 x_2^2$ rotating at the velocity $\Omega >0$, where $\Lambda\ge 1$ and $(x_1, x_2)\in R^2$. We focus on the case where…
We consider two-dimensional Bose-Einstein condensates with attractive interaction, described by the Gross-Pitaevskii functional. Minimizers of this functional exist only if the interaction strength $a$ satisfies $a < a^*= \|Q\|_2^2$, where…
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…
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation. For different initial vortex configurations we calculate…
Vortex nucleation in a Bose-Einstein condensate subject to a stirring potential is studied numerically using the zero-temperature, two-dimensional Gross-Pitaevskii equation. It is found that this theory is able to describe the creation of…
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as $ 1 / \eps^2 $ we consider the asymptotic regime $ \eps \to 0 $ with the…
This paper is concerned with the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensations (BECs) with attractive interactions in a bounded domain $\mathcal{D}\subset \mathbb{R}^2$. It is shown that,…
We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevksii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven…
We theoretically examine the rotation of an atomic Bose-Einstein condensate in an elliptical trap, both in the absence and presence of a quantized vortex. Two methods of introducing the rotating potential are considered - adiabatically…
The state of a rotating Bose-Einstein condensate in a harmonic trap is modeled by a wave function that minimizes the Gross-Pitaevskii functional. The resulting minimization problem has two new features compared to other similar functionals…
We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The…
We study the stability of vortices in a binary system of Bose-Einstein condensates, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we…
We investigate minimal energy solutions with vortices for an interacting Bose-Einstein condensate in a rotating trap. The atoms are strongly confined along the axis of rotation z, leading to an effective 2D situation in the x-y plane. We…
We study the fast rotation limit for a Bose-Einstein condensate in a quadratic plus quartic confining potential within the framework of the two dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to infinity with a…
For a Bose-Einstein condensate placed in a rotating trap and confined in the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas Fermi regime. We investigate an asymptotic development of the energy, the…