209 research outputs found
Coupling between magnetic field and curvature in Heisenberg spins on surfaces with rotational symmetry
We study the nonlinear -model in an external magnetic field applied
on curved surfaces with rotational symmetry. The Euler-Lagrange equations
derived from the Hamiltonian yield the double sine-Gordon equation (DSG)
provided the magnetic field is tuned with the curvature of the surface. A
skyrmion appears like a solution for this model and surface deformations
are predicted at the sector where the spins point in the opposite direction to
the magnetic field. We also study some specific examples by applying the model
on three rotationally symmetric surfaces: the cylinder, the catenoid and the
hyperboloid. The coupling between a magnetic field and the curvature of the
substract is an interesting result and we believe that this issue may be
relevant to be applied in condensed matter systems, e.g., superconductors,
nematic liquid crystals, graphene and topological insulators.Comment: To be published in Physics Letters
Born-Infeld particles and Dirichlet p-branes
Born-Infeld theory admits finite energy point particle solutions with
-function sources, BIons. I discuss their role in the theory of
Dirichlet -branes as the ends of strings intersecting the brane when the
effects of gravity are ignored. There are also topologically non-trivial
electrically neutral catenoidal solutions looking like two -branes joined by
a throat. The general solution is a non-singular deformation of the catenoid if
the charge is not too large and a singular deformation of the BIon solution for
charges above that limit. The intermediate solution is BPS and Coulomb-like.
Performing a duality rotation we obtain monopole solutions, the BPS limit being
a solution of the abelian Bogolmol'nyi equations. The situation closely
resembles that of sub and super extreme black-brane solutions of the
supergravity theories. I also show that certain special Lagrangian submanifolds
of , , may be regarded as supersymmetric configurations
consisting of -branes at angles joined by throats which are the sources of
global monopoles. Vortex solutions are also exhibited.Comment: 40 pages Latex file, no figure
On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry
We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two
kinds of excitations are considered. The first is given by the isotropic
regime, yielding the sine-Gordon equation and -solitons are predicted. The
second one is given by the XY model, leading to a vortex turning around the
surface. Helical states are also considered, however, topological arguments can
not be used to ensure its stability. The energy and the anisotropy parameter
which stabilizes the vortex state are explicitly calculated for two surfaces:
catenoid and hyperboloid. The results show that the anisotropy and the vortex
energy depends on the underlying geometry.Comment: 10 pages, 2 figures, Accepted for publication in Phys. Lett A (2013
D-Branes and their Absorptivity in Born-Infeld Theory
Standard methods of nonlinear dynamics are used to investigate the stability
of particles, branes and D-branes of abelian Born-Infeld theory. In particular
the equation of small fluctuations about the D-brane is derived and converted
into a modified Mathieu equation and - complementing earlier low-energy
investigations in the case of the dilaton-axion system - studied in the
high-energy domain. Explicit expressions are derived for the S-matrix and
absorption and reflection amplitudes of the scalar fluctuation in the presence
of the D-brane. The results confirm physical expectations and numerical studies
of others. With the derivation and use of the (hitherto practically unknown)
high energy expansion of the Floquet exponent our considerations also close a
gap in earlier treatments of the Mathieu equation.Comment: latex, 26 pages, 4 figures, one reference added, to appear in Nucl.
Phys.
A Note on Tachyons in the System
The periodic bounce of Born-Infeld theory of -branes is derived, and the
BPS limit of infinite period is discussed as an example of tachyon
condensation. The explicit bounce solution to the Born--Infeld action is
interpreted as an unstable fundamental string stretched between the brane and
its antibrane.Comment: 10 pages, 2 figures. v2: minor changes, acknowledgement added; v3:
explanations and references added. Final version to appear in Mod. Phys.
Lett.
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