86 research outputs found
Bose-Einstein condensate: critical velocities and energy diagrams in the Thomas-Fermi regime
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 critical velocities of nucleation of vortices with respect to a small
parameter \ep and the location of vortices. The limit \ep going to zero
corresponds to the Thomas Fermi regime. The non-dimensionalized energy is
similar to the Ginzburg-Landau energy for superconductors in the high-kappa
high-field limit and our estimates rely on techniques developed for this latter
problem. We also take the advantage of this similarity to develop a numerical
algorithm for computing the Bose-Einstein vortices. Numerical results and
energy diagrams are presented.Comment: 10pages 9 figure
Rotation of a Bose-Einstein Condensate held under a toroidal trap
The aim of this paper is to perform a numerical and analytical study of a
rotating Bose Einstein condensate placed in a harmonic plus Gaussian trap,
following the experiments of \cite{bssd}. The rotational frequency has
to stay below the trapping frequency of the harmonic potential and we find that
the condensate has an annular shape containing a triangular vortex lattice. As
approaches , the width of the condensate and the circulation
inside the central hole get large. We are able to provide analytical estimates
of the size of the condensate and the circulation both in the lowest Landau
level limit and the Thomas-Fermi limit, providing an analysis that is
consistent with experiment
Bifurcation problems for Ginzburg-Landau equations and applications to Bose Einstein condensates
3rd cycl
Pinning phenomena in the Ginzburg-Landau Model of Superconductivity
We study the Ginzburg-Landau energy of superconductors with a term a_\ep
modelling the pinning of vortices by impurities in the limit of a large
Ginzburg-Landau parameter \kappa=1/\ep. The function a_\ep is oscillating
between 1/2 and 1 with a scale which may tend to 0 as tends to
infinity.
Our aim is to understand that in the large limit, stable
configurations should correspond to vortices pinned at the minimum of a_\ep
and to derive the limiting homogenized free-boundary problem which arises for
the magnetic field in replacement of the London equation.
The method and techniques that we use are inspired from those of
Sandier-Serfaty (in which the case a_\ep \equiv 1 was treated) and based on
energy estimates, convergence of measures and construction of approximate
solutions. Because of the term a_\ep(x) in the equations, we also need
homogenization theory to describe the fact that the impurities, hence the
vortices, form a homogenized medium in the material.Comment: 40 page
A classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate
We classify the ground states and topological defects of a rotating
two-component condensate when varying several parameters: the intracomponent
coupling strengths, the intercomponent coupling strength and the particle
numbers.No restriction is placed on the masses or trapping frequencies of the
individual components. We present numerical phase diagrams which show the
boundaries between the regions of coexistence, spatial separation and symmetry
breaking. Defects such as triangular coreless vortex lattices, square coreless
vortex lattices and giant skyrmions are classified. Various aspects of the
phase diagrams are analytically justified thanks to a non-linear model
that describes the condensate in terms of the total density and a pseudo-spin
representation
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