101 research outputs found
Vortex Mass in a Superfluid
We consider the inertial mass of a vortex in a superfluid. We obtain a vortex
mass that is well defined and is determined microscopically and
self-consistently by the elementary excitation energy of the kelvon
quasiparticle localised within the vortex core. The obtained result for the
vortex mass is found to be consistent with experimental observations on
superfluid quantum gases and vortex rings in water. We propose a method to
measure the inertial rest mass and Berry phase of a vortex in superfluid Bose
and Fermi gases.Comment: 12 pages, 1 figur
The ground state of a GrossāPitaevskii energy with general potential in the ThomasāFermi limit
We study the ground state which minimizes a GrossāPitaevskii
energy with general non-radial trapping potential, under the unit mass constraint, in the ThomasāFermi limit where a small parameter tends to 0. This ground state plays an important role in the mathematical treatment of recent
experiments on the phenomenon of BoseāEinstein condensation, and in the study of various types of solutions of nonhomogeneous defocusing nonlinear Schrodinger equations. Many of these applications require delicate estimates
for the behavior of the ground state near the boundary of the condensate, as the singular parameter tends to zero, in the vicinity of which the ground state has irregular behavior in the form of a steep corner layer. In particular, the role of this layer is important in order to detect the presence of vortices in the small density region of the
condensate, understand the superļ¬uid ļ¬ow around an obstacle, and also has a leading order contribution in the energy. In contrast to previous approaches, we utilize a perturbation argument to go beyond the classical ThomasāFermi
approximation and accurately approximate the layer by the HastingsāMcLeod solution of the PainleveāII equation. This settles an open problem, answered very recently only for the special case of the model harmonic potential. In fact, we even improve upon previous results that relied heavily on the radial symmetry of the potential trap. Moreover, we show that the ground state has the maximal regularity available,
namely it remains uniformly bounded in the
1/2-Holder norm, which is the exact Holder regularity of the singular limit proļ¬le, as the singular parameter tends to zero. Our study is highly motivated by an interesting open problem posed recently by Aftalion, Jerrard, and Royo-Letelier, and an open question of Gallo and Pelinovsky,
concerning the removal of the radial symmetry assumption from the potential trap
The effective action and equations of motion of curved local and global vortices: Role of the field excitations
The effective actions for both local and global curved vortices are derived,
based on the derivative expansion of the corresponding field theoretic actions
of the nonrelativistic Abelian Higgs and Goldstone models. The role of
excitations of the modulus and the phase of the scalar field and of the gauge
field (the Bogolyubov-Anderson mode) emitted and reabsorbed by vortices is
elucidated. In case of the local (gauge) magnetic vortex, they are necessary
for cancellation of the long distance divergence when using the transverse form
of the electric gauge field strength of the background field. In case of global
vortex taking them into account results in the Greiter-Wilczek-Witten form of
the effective action for the Goldstone mode. The expressions for transverse
Magnus-like force and the vortex effective mass for both local and global
vortices are found. The equations of motion of both type of vortices including
the terms due to the field excitations are obtained and solved in cases of
large and small contour displacements.Comment: 16 pages, no figures; accepted for publication in Int. Journ. Mod.
Phys.
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