40 research outputs found
Dynamical role of anyonic excitation statistics in rapidly rotating Bose gases
We show that for rotating harmonically trapped Bose gases in a fractional
quantum Hall state, the anyonic excitation statistics in the rotating gas can
effectively play a {\em dynamical} role. For particular values of the
two-dimensional coupling constant , where is a
positive integer, the system becomes a noninteracting gas of anyons, with
exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter
equations. Attractive Bose gases under rapid rotation thus can be stabilized in
the thermodynamic limit due to the anyonic statistics of their quasiparticle
excitations.Comment: 4 pages of RevTex4; as published in Physical Review Letter
Simple Vortex States in Films of Type-I Ginzburg-Landau Superconductor
Sufficiently thin films of type-I superconductor in a perpendicular magnetic
field exhibit a triangular vortex lattice, while thick films develop an
intermediate state. To elucidate what happens between these two regimes,
precise numerical calculations have been made within Ginzburg-Landau theory at
and 0.25 for a variety of vortex lattice structures with one flux
quantum per unit cell. The phase diagram in the space of mean induction and
film thickness includes a narrow wedge in which a square lattice is stable,
surrounded by the domain of stability of the triangular lattice at thinner
films/lower fields and, on the other side, rectangular lattices with
continuously varying aspect ratio. The vortex lattice has an anomalously small
shear modulus within and close to the square lattice phase.Comment: 21 pages, 6 figure
Vortex solutions in the noncommutative torus
Vortex configurations in the two-dimensional torus are considered in
noncommutative space. We analyze the BPS equations of the Abelian Higgs model.
Numerical solutions are constructed for the self-dual and anti-self dual cases
by extending an algorithm originally developed for ordinary commutative space.
We work within the Fock space approach to noncommutative theories and the
Moyal-Weyl connection is used in the final stage to express the solutions in
configuration space.Comment: 18 pages, 5 figure
Vortices in Ginzburg-Landau billiards
We present an analysis of the Ginzburg-Landau equations for the description
of a two-dimensional superconductor in a bounded domain. Using the properties
of a special integrability point of these equations which allows vortex
solutions, we obtain a closed expression for the energy of the superconductor.
The role of the boundary of the system is to provide a selection mechanism
for the number of vortices.
A geometrical interpretation of these results is presented and they are
applied to the analysis of the magnetization recently measured on small
superconducting disks. Problems related to the interaction and nucleation of
vortices are discussed.Comment: RevTex, 17 pages, 3 eps figure
Dual Instantons
We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear
model to a dual theory where they then appear as nontopological
solitons. They are stationary points of the Euclidean action in the dual
theory, and moreover, the dual action and the O(3)-nonlinear model
action agree on shell.Comment: 13 page
A BPS Interpretation of Shape Invariance
We show that shape invariance appears when a quantum mechanical model is
invariant under a centrally extended superalgebra endowed with an additional
symmetry generator, which we dub the shift operator. The familiar mathematical
and physical results of shape invariance then arise from the BPS structure
associated with this shift operator. The shift operator also ensures that there
is a one-to-one correspondence between the energy levels of such a model and
the energies of the BPS-saturating states. These findings thus provide a more
comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe
Macroscopic models for superconductivity
This paper reviews the derivation of some macroscopic models for superconductivity and also some of the mathematical challenges posed by these models. The paper begins by exploring certain analogies between phase changes in superconductors and those in solidification and melting. However, it is soon found that there are severe limitations on the range of validity of these analogies and outside this range many interesting open questions can be posed about the solutions to the macroscopic models
Exploring the vicinity of the Bogomol'nyi-Prasad-Sommerfield bound
We investigate systems of real scalar fields in bidimensional spacetime,
dealing with potentials that are small modifications of potentials that admit
supersymmetric extensions. The modifications are controlled by a real
parameter, which allows implementing a perturbation procedure when such
parameter is small. The approach allows obtaining the energy and topological
charge in closed forms, up to first order in the parameter. We illustrate the
procedure with some examples. In particular, we show how to remove the
degeneracy in energy for the one-field and the two-field solutions that appear
in a model of two real scalar fields.Comment: Revtex, 9 pages, To be published in J. Phys.
Vortex Dynamics in Selfdual Maxwell-Higgs Systems with Uniform Background Electric Charge Density
We introduce selfdual Maxwell-Higgs systems with uniform background electric
charge density and show that the selfdual equations satisfied by topological
vortices can be reduced to the original Bogomol'nyi equations without any
background. These vortices are shown to carry no spin but to feel the Magnus
force due to the shielding charge carried by the Higgs field. We also study the
dynamics of slowly moving vortices and show that the spin-statistics theorem
holds to our vortices.Comment: 24 pages + 2 figures ( not included), Cu-TP-611, IASSNS-HEP-93/33,
NSF-ITP-93-13
On Matrix Superpotential and Three-Component Normal Modes
We consider the supersymmetric quantum mechanics (SUSY QM) with three-
component normal modes for the Bogomol'nyi-Prasad-Sommerfield (BPS) states. An
explicit form of the SUSY QM matrix superpotential is presented and the
corresponding three-component bosonic zero-mode eigenfunction is investigated.Comment: 17 pages, no figure. Paper accepted for publication in Journal of
Physics A: Mathematical and Theoretica