2,860 research outputs found
Noncommutative Electrodynamics with covariant coordinates
We study Noncommutative Electrodynamics using the concept of covariant
coordinates. We propose a scheme for interpreting the formalism and construct
two basic examples, a constant field and a plane wave. Superposing these two,
we find a modification of the dispersion relation. Our results differ from
those obtained via the Seiberg-Witten map.Comment: 5 pages, published versio
Self-organisation to criticality in a system without conservation law
We numerically investigate the approach to the stationary state in the
nonconservative Olami-Feder-Christensen (OFC) model for earthquakes. Starting
from initially random configurations, we monitor the average earthquake size in
different portions of the system as a function of time (the time is defined as
the input energy per site in the system). We find that the process of
self-organisation develops from the boundaries of the system and it is
controlled by a dynamical critical exponent z~1.3 that appears to be universal
over a range of dissipation levels of the local dynamics. We show moreover that
the transient time of the system scales with system size L as . We argue that the (non-trivial) scaling of the transient time in the
OFC model is associated to the establishment of long-range spatial correlations
in the steady state.Comment: 10 pages, 6 figures; accepted for publication in Journal of Physics
Radiation Damping of a BPS Monopole; an Implication to S-duality
The radiation reaction of a BPS monopole in the presence of incident
electromagnetic waves as well as massless Higgs waves is analyzed classically.
The reactive forces are compared to those of boson that is interpreted as a
dual partner of the BPS monopole. It is shown that the damping of acceleration
is dual to each other, while in the case of finite size effects the duality is
broken explicitly. Their implications on the duality are discussed.Comment: 20 pages, uses revtex, changes in reference
Covariant Coordinate Transformations on Noncommutative Space
We show how to define gauge-covariant coordinate transformations on a
noncommuting space. The construction uses the Seiberg-Witten equation and
generalizes similar results for commuting coordinates.Comment: 11 pages, LaTeX; email correspondence to [email protected]
Ultrametricity and Memory in a Solvable Model of Self-Organized Criticality
Slowly driven dissipative systems may evolve to a critical state where long
periods of apparent equilibrium are punctuated by intermittent avalanches of
activity. We present a self-organized critical model of punctuated equilibrium
behavior in the context of biological evolution, and solve it in the limit that
the number of independent traits for each species diverges. We derive an exact
equation of motion for the avalanche dynamics from the microscopic rules. In
the continuum limit, avalanches propagate via a diffusion equation with a
nonlocal, history-dependent potential representing memory. This nonlocal
potential gives rise to a non-Gaussian (fat) tail for the subdiffusive
spreading of activity. The probability for the activity to spread beyond a
distance in time decays as for . The potential
represents a hierarchy of time scales that is dynamically generated by the
ultrametric structure of avalanches, which can be quantified in terms of
``backward'' avalanches. In addition, a number of other correlation functions
characterizing the punctuated equilibrium dynamics are determined exactly.Comment: 44 pages, Revtex, (12 ps-figures included
Melting of hexagonal skyrmion states in chiral magnets
Skyrmions are spiral structures observed in thin films of certain magnetic materials (Uchida et al 2006 Science 311 359â61). Of the phases allowed by the crystalline symmetries of these materials (Yi et al 2009 Phys. Rev. B 80 054416), only the hexagonally packed phases (SCh) have been observed. Here the melting of the SCh phase is investigated using Monte Carlo simulations. In addition to the usual measure of skyrmion density, chiral charge, a morphological measure is considered. In doing so it is shown that the low-temperature reduction in chiral charge is associated with a change in skyrmion profiles rather than skyrmion destruction. At higher temperatures, the loss of six-fold symmetry is associated with the appearance of elongated skyrmions that disrupt the hexagonal packing
Seiberg-Witten Transforms of Noncommutative Solitons
We evaluate the Seiberg-Witten map for solitons and instantons in
noncommutative gauge theories in various dimensions. We show that solitons
constructed using the projection operators have delta-function supports when
expressed in the commutative variables. This gives a precise identification of
the moduli of these solutions as locations of branes. On the other hand, an
instanton solution in four dimensions allows deformation away from the
projection operator construction. We evaluate the Seiberg-Witten transform of
the U(2) instanton and show that it has a finite size determined by the
noncommutative scale and by the deformation parameter \rho. For large \rho, the
profile of the D0-brane density of the instanton agrees surprisingly well with
that of the BPST instanton on commutative space.Comment: 29 pages, LaTeX; comments added, typos corrected, and a reference
added; comments added, typos correcte
Supertubes in Matrix model and DBI action
We show the equivalence between the supertube solutions with an arbitrary
cross section in two different actions, the DBI action for the D2-brane and the
matrix model action for the D0-branes. More precisely, the equivalence between
the supertubes in the D2-brane picture and the D0-brane picture is shown in the
boundary state formalism which is valid for all order in \alpha'. This is an
application of the method using the infinitely many D0-branes and
anti-D0-branes which was used to show other equivalence relations between two
seemingly different D-brane systems, including the D-brane realization of the
ADHM construction of instanton. We also apply this method to the superfunnel
type solutions successfully.Comment: 24 pages, references added, version to appear in JHE
Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory
We consider the non-relativistic superconformal U(N) X U(N) Chern-Simons
theory with level (k,-k) possessing fourteen supersymmetries. We obtain an
exact four-point scattering amplitude of the theory to all orders in 1/N and
1/k and prove that the scattering amplitude becomes trivial when k=1 and 2. We
confirm this amplitude to one-loop order by using an explicit field theoretic
computation and show that the beta function for the contact interaction
vanishes to the one-loop order, which is consistent with the quantum conformal
invariance of the underlying theory.Comment: 16 page
Counting Yang-Mills Dyons with Index Theorems
We count the supersymmetric bound states of many distinct BPS monopoles in
N=4 Yang-Mills theories and in pure N=2 Yang-Mills theories. The novelty here
is that we work in generic Coulombic vacua where more than one adjoint Higgs
fields are turned on. The number of purely magnetic bound states is again found
to be consistent with the electromagnetic duality of the N=4 SU(n) theory, as
expected. We also count dyons of generic electric charges, which correspond to
1/4 BPS dyons in N=4 theories and 1/2 BPS dyons in N=2 theories. Surprisingly,
the degeneracy of dyons is typically much larger than would be accounted for by
a single supermultiplet of appropriate angular momentum, implying many
supermutiplets of the same charge and the same mass.Comment: 34 pages, 1 figure, LaTe
- âŠ