Related papers: Thomas-Fermi Approximation for a Condensate with H…
A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed…
We consider the ground state of a trapped Bose-Einstein condensate in two dimensions. In the mean-field approximation, the ground state density profile satisfies the Gross-Pitaevskii equation. We compute the leading quantum corrections to…
We study harmonically trapped two-species Bose-Einstein condensates within the Gross-Pitaevskii formalism. By invoking the Thomas-Fermi approximation, we derive an analytical solution for the miscible ground state in a particular region of…
In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate, or equivalently, by the hydrodynamic equations for the number density and the current…
By incorporating the zero-point energy contribution we derive simple and accurate extensions of the usual Thomas-Fermi (TF) expressions for the ground-state properties of trapped Bose-Einstein condensates that remain valid for an arbitrary…
For the stationary Gross-Pitaevskii equation with harmonic real and linear imaginary potentials in the space of one dimension, we study the ground state in the limit of large densities (large chemical potentials), where the solution…
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…
Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the…
We investigate a harmonically trapped two-component Bose--Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra- and inter-species interactions. We derive analytically a universal…
We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic…
We study a binary mixture of Bose-Einstein condensates, confined in a generic potential, in the Thomas-Fermi approximation. We search for the zero-temperature ground state of the system, both in the case of fixed numbers of particles and…
We study the minimizers of a magnetic 2D non-linear Schr\"odinger energy functional in a quadratic trapping potential, describing a rotating Bose-Einstein condensate. We derive an effective Thomas-Fermi-like model in the rapidly rotating…
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 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…
We study the stationary solution of an atomic Bose-Einstein condensate coupled coherently to a molecular condensate with both repulsive and attractive interspecies interactions confined in an isotropic harmonic trap. We use the Thomas-Fermi…
An approximate solution to the Gross-Pitaevskii equation for Bose-Einstein condensate in a spherical harmonic trap is suggested, which is valid in the whole interval of the coupling parameter, correctly interpolating between weak-coupling…
These notes present simple theoretical approaches to study Bose-Einstein condensation in trapped atomic gases and their comparison to recent experimental results : - the ideal Bose gas model - Fermi pseudopotential to model the atomic…
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 cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of…
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…