40 research outputs found
A class of kinks in SU(N)\times Z_2
In a classical, quartic field theory with symmetry, a
class of kink solutions can be found analytically for one special choice of
parameters. We construct these solutions and determine their energies. In the
limit , the energy of the kink is equal to that of a kink in a
model with the same mass parameter and quartic coupling (coefficient of
). We prove the stability of the solutions to small
perturbations but global stability remains unproven. We then argue that the
continuum of choices for the boundary conditions leads to a whole space of kink
solutions. The kinks in this space occur in classes that are determined by the
chosen boundary conditions. Each class is described by the coset space
where is the unbroken symmetry group and is the symmetry group that
leaves the kink solution invariant.Comment: 7 pages; included discussion of gauge fields and other improvement
Static intervortex forces
A point particle approximation to the classical dynamics of well separated
vortices of the abelian Higgs model is developed. A static vortex is
asymptotically identical to a solution of the linearized field theory (a
Klein-Gordon/Proca theory) in the presence of a singular point source at the
vortex centre. It is shown that this source is a composite scalar monopole and
magnetic dipole, and the respective charges are determined numerically for
various values of the coupling constant. The interaction potential of two well
separated vortices is computed by calculating the interaction Lagrangian of two
such point sources in the linear theory. The potential is used to model type II
vortex scattering.Comment: Much shorter (10 pages) published version, new titl
A dual point description of mesoscopic superconductors
We present an analysis of the magnetic response of a mesoscopic
superconductor, i.e. a system of sizes comparable to the coherence length and
to the London penetration depth. Our approach is based on special properties of
the two dimensional Ginzburg-Landau equations, satisfied at the dual point
Closed expressions for the free energy and the
magnetization of the superconductor are derived. A perturbative analysis in the
vicinity of the dual point allows us to take into account vortex interactions,
using a new scaling result for the free energy. In order to characterize the
vortex/current interactions, we study vortex configurations that are out of
thermodynamical equilibrium. Our predictions agree with the results of recent
experiments performed on mesoscopic aluminium disks.Comment: revtex, 20 pages, 9 figure
Vortex lattice stability in the SO(5) model
We study the energetics of superconducting vortices in the SO(5) model for
high- materials proposed by Zhang. We show that for a wide range of
parameters normally corresponding to type II superconductivity, the free energy
per unit flux \FF(m) of a vortex with flux quanta is a decreasing
function of , provided the doping is close to its critical value. This
implies that the Abrikosov lattice is unstable, a behaviour typical of type I
superconductors. For dopings far from the critical value, \FF(m) can become
very flat, indicating a less rigid vortex lattice, which would melt at a lower
temperature than expected for a BCS superconductor.Comment: 4 pp, revtex, 5 figure
New vortex solution in SU(3) gauge-Higgs theory
Following a brief review of known vortex solutions in SU(N) gauge-adjoint
Higgs theories we show the existence of a new ``minimal'' vortex solution in
SU(3) gauge theory with two adjoint Higgs bosons. At a critical coupling the
vortex decouples into two abelian vortices, satisfying Bogomol'nyi type, first
order, field equations. The exact value of the vortex energy (per unit length)
is found in terms of the topological charge that equals to the N=2
supersymmetric charge, at the critical coupling. The critical coupling signals
the increase of the underlying supersymmetry.Comment: 15 page
Moving lattice kinks and pulses: an inverse method
We develop a general mapping from given kink or pulse shaped travelling-wave
solutions including their velocity to the equations of motion on
one-dimensional lattices which support these solutions. We apply this mapping -
by definition an inverse method - to acoustic solitons in chains with nonlinear
intersite interactions, to nonlinear Klein-Gordon chains, to reaction-diffusion
equations and to discrete nonlinear Schr\"odinger systems. Potential functions
can be found in at least a unique way provided the pulse shape is reflection
symmetric and pulse and kink shapes are at least functions. For kinks we
discuss the relation of our results to the problem of a Peierls-Nabarro
potential and continuous symmetries. We then generalize our method to higher
dimensional lattices for reaction-diffusion systems. We find that increasing
also the number of components easily allows for moving solutions.Comment: 15 pages, 5 figure
Dyons in N=4 Gauged Supergravity
We study monopole and dyon solutions to the equations of motion of the
bosonic sector of N = 4 gauged supergravity in four dimensional space-time. A
static, spherically symmetric ansatz for the metric, gauge fields, dilaton and
axion leads to soliton solutions which, in the electrically charged case, have
compact spatial sections. Both analytical and numerical results for the
solutions are presented.Comment: 12 pages, 7 figures. Minor changes, references adde
Mesoscopic superconductors in the London limit: equilibrium properties and metastability
We present a study of the behaviour of metastable vortex states in mesoscopic
superconductors. Our analysis relies on the London limit within which it is
possible to derive closed analytical expressions for the magnetic field and the
Gibbs free energy. We consider in particular the situation where the vortices
are symmetrically distributed along a closed ring. There, we obtain expressions
for the confining Bean-Livingston barrier and for the magnetization which turns
out to be paramagnetic away from thermodynamic equilibrium. At low temperature,
the barrier is high enough for this regime to be observable. We propose also a
local description of both thermodynamic and metastable states based on
elementary topological considerations; we find structural phase transitions of
vortex patterns between these metastable states and we calculate the
corresponding critical fields.Comment: 24 pages, 20 figure
SU(5) monopoles and non-abelian black holes
We construct spherically and axially symmetric monopoles in SU(5)
Yang-Mills-Higgs theory both in flat and curved space as well as spherical and
axial non-abelian, ''hairy'' black holes. We find that in analogy to the SU(2)
case, the flat space monopoles are either non-interacting (in the BPS limit) or
repelling. In curved space, however, gravity is able to overcome the repulsion
for suitable choices of the Higgs coupling constants and the gravitational
coupling. In addition, we confirm that indeed all qualitative features of
(gravitating) SU(2) monopoles are found as well in the SU(5) case. For the
non-abelian black holes, we compare the behaviour of the solutions in the BPS
limit with that for non-vanishing Higgs self-coupling constants.Comment: 14 Revtex pages, 9 PS-figure
Vortex Interactions and Thermally Induced Crossover from Type-I to Type-II Superconductivity
We have computed the effective interaction between vortices in the
Ginzburg-Landau model from large-scale Monte-Carlo simulations, taking thermal
fluctuations of matter fields and gauge fields fully into account close to the
critical temperature. We find a change, in the form of a crossover, from
attractive to repulsive effective vortex interactions in an intermediate range
of Ginzburg-Landau parameters upon increasing
the temperature in the superconducting state. This corresponds to a thermally
induced crossover from \typeI to \typeII superconductivity around a temperature
, which we map out in the vicinity of the
metal-to-superconductor transition. In order to see this crossover, it is
essential to include amplitude fluctuations of the matter field, in addition to
phase-fluctuations and gauge-field fluctuations. We present a simple physical
picture of the crossover, and relate it to observations in \metal{Ta} and
\metal{Nb} elemental superconductors which have low-temperature values of
in the relevant range.Comment: 9 pages, 6 figures. Accepted for publication in Physical Review