86 research outputs found
Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps
We extend the results of a previous paper on the Gross-Pitaevskii description
of rotating Bose-Einstein condensates in two-dimensional traps to confining
potentials of the form V(r) = r^s, . Writing the coupling constant
as we study the limit . We derive rigorously the
leading asymptotics of the ground state energy and the density profile when the
rotation velocity \Omega tends to infinity as a power of . The case
of asymptotically homogeneous potentials is also discussed.Comment: LaTex2e, 16 page
Vortex Phases of Rotating Superfluids
We report on the first mathematically rigorous proofs of a transition to a
giant vortex state of a superfluid in rotating anharmonic traps. The analysis
is carried out within two-dimensional Gross-Pitaevskii theory at large coupling
constant and large rotational velocity and is based on precise asymptotic
estimates on the ground state energy. An interesting aspect is a significant
difference between 'soft' anharmonic traps (like a quartic plus quadratic
trapping potential) and traps with a fixed boundary. In the former case
vortices persist in the bulk until the width of the annulus becomes comparable
to the size of the vortex cores. In the second case the transition already
takes place in a parameter regime where the size of vortices is very small
relative to the width of the annulus. Moreover, the density profiles in the
annulus are different in the two cases. In both cases rotational symmetry of
the density in a true ground state is broken, even though a symmetric
variational ansatz gives an excellent approximation to the energy.Comment: For the Proceedings of 21st International Laser Physics Workshop,
Calgary, July 23-27, 201
Modular Groups of Quantum Fields in Thermal States
For a quantum field in a thermal equilibrium state we discuss the group
generated by time translations and the modular action associated with an
algebra invariant under half-sided translations. The modular flows associated
with the algebras of the forward light cone and a space-like wedge admit a
simple geometric description in two dimensional models that factorize in
light-cone coordinates. At large distances from the domain boundary compared to
the inverse temperature the flow pattern is essentially the same as time
translations, whereas the zero temperature results are approximately reproduced
close to the edge of the wedge and the apex of the cone. Associated with each
domain there is also a one parameter group with a positive generator, for which
the thermal state is a ground state. Formally, this may be regarded as a
certain converse of the Unruh-effect.Comment: 28 pages, 4 figure
Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps
We study a rotating Bose-Einstein Condensate in a strongly anharmonic trap
(flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii
theory. We write the coupling constant for the interactions between the gas
atoms as and we are interested in the limit (TF
limit) with the angular velocity depending on . We derive
rigorously the leading asymptotics of the ground state energy and the density
profile when tends to infinity as a power of . If
a ``hole'' (i.e., a region where the
density becomes exponentially small as ) develops for
above a certain critical value. If
the hole essentially exhausts the container and a ``giant vortex'' develops
with the density concentrated in a thin layer at the boundary. While we do not
analyse the detailed vortex structure we prove that rotational symmetry is
broken in the ground state for .Comment: LaTex2e, 28 pages, revised version to be published in Journal of
Mathematical Physic
Disordered Bose Einstein Condensates with Interaction in One Dimension
We study the effects of random scatterers on the ground state of the
one-dimensional Lieb-Liniger model of interacting bosons on the unit interval
in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation
survives even a strong random potential with a high density of scatterers. The
character of the wave function of the condensate, however, depends in an
essential way on the interplay between randomness and the strength of the
two-body interaction. For low density of scatterers or strong interactions the
wave function extends over the whole interval. High density of scatterers and
weak interaction, on the other hand, leads to localization of the wave function
in a fragmented subset of the interval
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