Related papers: Projected Gross-Pitaevskii equation for ring-shape…
For a Bose-Einstein condensate placed in a rotating trap, we give a simplified expression of the Gross-Pitaevskii energy in the Thomas Fermi regime, which only depends on the number and shape of the vortex lines. Then we check numerically…
The Gross-Pitaevskii equation (GP), that describes the wave function of a number of coherent Bose particles contained in a trap, contains the cube of the normalized wave function, times a factor proportional to the number of coherent atoms.…
We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii…
We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ…
We consider the ground state of a harmonically trapped Bose-Einstein condensate within the Gross-Pitaevskii theory including the effective-range corrections for a two-body zero-range potential. The resulting non-linear Schr\"odinger…
In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the…
The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external $\mathcal{PT}$-symmetric double-delta potential. We study its linear variant with…
The magnetically induced Richtmyer-Meshkov instability in a two-component Bose-Einstein condensate is investigated. We construct and study analytical models describing the development of the instability at both the linear and nonlinear…
We study a modified three-dimensional Gross-Pitaevski equation that describes a static impurity in a dipolar Bose-Einstein condensate (BEC). Our focus is on the interplay between the shape of the impurity and the anisotropy of the medium…
We study the interplay between the anisotropy of the dipole-dipole interaction and confinement in a curved geometry by means of the extended Gross-Pitaevskii equation, which allows us to characterize the ground state of a dipolar Bose gas…
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise.…
We propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non…
We investigate a Bose-Einstein condensate held in a quasi-one-dimensional Wannier-Stark lattice which is a combination of linear potential with an accelerated optical lattice. It is demonstrated that the system can be reduced to a…
In this article a perturbative solution of the Gross-Pitaevskii(GP) equation in the $D$-dimensional space $R^D$ with a general external potential is studied. The solution describes the condensate wave-function of a gas containing $N$ Bose…
We present a method for solving the stochastic projected Gross-Pitaevskii equation (SPGPE) for a three-dimensional Bose gas in a harmonic-oscillator trapping potential. The SPGPE contains the challenge of both accurately evolving all modes…
Considering an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a toroidal trap, we find that the system undergoes a phase transition from a uniform to a localized state, as the magnitude of the…
Angular momentum can be transferred to a trapped Bose-Einstein condensate by distorting its shape with an external rotating field, provided the rotational frequency is larger than a critical frequency fixed by the energy and angular…
We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the…
We study the time-evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. Under a physically motivated assumption on the energy of the initial data, we show that condensation is preserved by the many-body…
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…