11,566 research outputs found
The use of the Winograd matrix multiplication algorithm in digital multispectral processing
The Winograd procedure for matrix multiplication provides a method whereby general matrix products may be computed more efficiently than the normal method. The algorithm and the time savings that can be effected are described. A FORTRAN program is provided which performs a general matrix multiply according to this algorithm. A variation of this procedure that may be used to calculate Gaussian probability density functions is also described. It is shown how a time savings can be effected in this calculation. The extension of this method to other similar calculations should yield similar savings
Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra
We study the influence of phase matching on interference minima in high
harmonic spectra. We concentrate on structures in atoms due to interference of
different angular momentum channels during recombination. We use the Cooper
minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure
2d harmonic spectra in argon as a function of wavelength and angular
divergence. While we identify a clear CM in the spectrum when the target gas
jet is placed after the laser focus, we find that the appearance of the CM
varies with angular divergence and can even be completely washed out when the
gas jet is placed closer to the focus. We also show that the argon CM appears
at different wavelengths in harmonic and photo-absorption spectra measured
under conditions independent of any wavelength calibration. We model the
experiment with a simulation based on coupled solutions of the time-dependent
Schr\"odinger equation and the Maxwell wave equation, including both the single
atom response and macroscopic effects of propagation. The single atom
calculations confirm that the ground state of argon can be represented by its
field free symmetry, despite the strong laser field used in high harmonic
generation. Because of this, the CM structure in the harmonic spectrum can be
described as the interference of continuum and channels, whose relative
phase jumps by at the CM energy, resulting in a minimum shifted from the
photoionization result. We also show that the full calculations reproduce the
dependence of the CM on the macroscopic conditions. We calculate simple phase
matching factors as a function of harmonic order and explain our experimental
and theoretical observation in terms of the effect of phase matching on the
shape of the harmonic spectrum. Phase matching must be taken into account to
fully understand spectral features related to HHG spectroscopy
Alternativity and reciprocity in the Cayley-Dickson algebra
We calculate the eigenvalue \rho of the multiplication mapping R on the
Cayley-Dickson algebra A_n. If the element in A_n is composed of a pair of
alternative elements in A_{n-1}, half the eigenvectors of R in A_n are still
eigenvectors in the subspace which is isomorphic to A_{n-1}.
The invariant under the reciprocal transformation A_n \times A_{n} \ni (x,y)
-> (-y,x) plays a fundamental role in simplifying the functional form of \rho.
If some physical field can be identified with the eigenspace of R, with an
injective map from the field to a scalar quantity (such as a mass) m, then
there is a one-to-one map \pi: m \mapsto \rho. As an example, the electro-weak
gauge field can be regarded as the eigenspace of R, where \pi implies that the
W-boson mass is less than the Z-boson mass, as in the standard model.Comment: To be published in J. Phys. A: Mathematical and Genera
Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase
We present an approximate gap equation for different crystalline structures
of the LOFF phase of high density QCD at T=0. This equation is derived by using
an effective condensate term obtained by averaging the inhomogeneous condensate
over distances of the order of the crystal lattice size. The approximation is
expected to work better far off any second order phase transition. As a
function of the difference of the chemical potentials of the up and down
quarks, , we get that the octahedron is energetically favored from
to , where is the gap for
the homogeneous phase, while in the range the face
centered cube prevails. At a first order phase
transition to the normal phase occurs.Comment: 11 pages, 5 figure
On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
We consider the highest-energy state in the su(1|1) sector of N=4 super
Yang-Mills theory containing operators of the form tr(Z^{L-M} \psi^M) where Z
is a complex scalar and \psi is a component of gaugino. We show that this state
corresponds to the operator tr(\psi^L) and can be viewed as an analogue of the
antiferromagnetic state in the su(2) sector. We find perturbative expansions of
the energy of this state in both weak and strong 't Hooft coupling regimes
using asymptotic gauge theory Bethe ansatz equations. We also discuss a
possible analog of this state in the conjectured string Bethe ansatz equations.Comment: 23 pages, Late
Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes
We compute one-loop S-matrix in the reduced sigma-model which describes AdS_5
x S^5 string theory in the near-flat-space limit. The result agrees with the
corresponding limit of the S-matrix in the full sigma-model, which demonstrates
the consistency of the reduction at the quantum level.Comment: 9 pages, 1 figure; v2: reference added; v3: misprint in (3.6)
corrected; v4: typo in (3.4) corrected; v5: new form of the actio
Chiral Loops and Ghost States in the Quenched Scalar Propagator
The scalar, isovector meson propagator is analyzed in quenched QCD, using the
MQA pole-shifting ansatz to study the chiral limit. In addition to the expected
short-range exponential falloff characteristic of a heavy scalar meson, the
propagator also exhibits a longer-range, negative metric contribution which
becomes pronounced for smaller quark masses. We show that this is a quenched
chiral loop effect associated with the anomalous structure of the
propagator in quenched QCD. Both the time dependence and the quark mass
dependence of this effect are well-described by a chiral loop diagram
corresponding to an intermediate state, which is light and
effectively of negative norm in the quenched approximation. The relevant
parameters of the effective Lagrangian describing the scalar sector of the
quenched theory are determined.Comment: 29 pages, 10 figures, Late
Thermodynamic properties of QCD in external magnetic fields
We consider the effect of strong external electromagnetic fields on
thermodynamic observables in QCD, through lattice simulations with 1+1+1
flavors of staggered quarks at physical quark masses. Continuum extrapolated
results are presented for the light quark condensates and for their tensor
polarizations, as functions of the temperature and the magnetic field. We find
the light condensates to undergo inverse magnetic catalysis in the transition
region, in a manner that the transition temperature decreases with growing
magnetic field. We also compare the results to other approaches and lattice
simulations. Furthermore, we relate the tensor polarization to the spin part of
the magnetic susceptibility of the QCD vacuum, and show that this contribution
is diamagnetic.Comment: 13 pages, 9 figures, talks presented by FB and GE at Xth Quark
Confinement and the Hadron Spectrum, 8-12 October 2012, TUM Campus Garching,
Munich, German
Magnetic Anisotropy of Co2+ as Signature of Intrinsic Ferromagnetism in ZnO:Co
We report on the magnetic properties of thoroughly characterized Zn1-xCoxO
epitaxial thin films, with low Co concentration, x=0.003-0.005. Magnetic and
EPR measurements, combined with crystal field theory, reveal that isolated Co2+
ions in ZnO possess a strong single ion anisotropy which leads to an "easy
plane" ferromagnetic state when the ferromagnetic Co-Co interaction is
considered. We suggest that the peculiarities of the magnetization process of
this state can be viewed as a signature of intrinsic ferromagnetism in ZnO:Co
materials.Comment: 4 pages, 4 figure
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