29,022 research outputs found
Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators
We present a matrix technique to obtain the spectrum and the analytical index
of some elliptic operators defined on compact Riemannian manifolds. The method
uses matrix representations of the derivative which yield exact values for the
derivative of a trigonometric polynomial. These matrices can be used to find
the exact spectrum of an elliptic operator in particular cases and in general,
to give insight into the properties of the solution of the spectral problem. As
examples, the analytical index and the eigenvalues of the Dirac operator on the
torus and on the sphere are obtained and as an application of this technique,
the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page
The Dyer-Roeder relation in a universe with particle production
We have obtained analytical exact solutions of the Dyer-Roeder equation in a
cosmological model where creation of particles occurs at the expenses of the
gravitational field. We discussed the influences of inhomogeneities in the path
of a light beam on the apparent diameter of astrophysical objects and consider
both redshift independent as redshift dependent distributions of the
inhomogeneities.Comment: 7 pages, 4 figures. Accepted to be published in the Astronomy and
Astrophysics Journa
Palindromic 3-stage splitting integrators, a roadmap
The implementation of multi-stage splitting integrators is essentially the
same as the implementation of the familiar Strang/Verlet method. Therefore
multi-stage formulas may be easily incorporated into software that now uses the
Strang/Verlet integrator. We study in detail the two-parameter family of
palindromic, three-stage splitting formulas and identify choices of parameters
that may outperform the Strang/Verlet method. One of these choices leads to a
method of effective order four suitable to integrate in time some partial
differential equations. Other choices may be seen as perturbations of the
Strang method that increase efficiency in molecular dynamics simulations and in
Hybrid Monte Carlo sampling.Comment: 20 pages, 8 figures, 2 table
Towards the lattice study of M-theory
We propose the Wilson discretization of the supersymmetric Yang-Mills Quantum
Mechanics as a lattice version of the matrix model of M-theory. An SU(2) model
is studied numerically in the quenched approximation for D=4. A clear signal
for the existence of two different phases is found and the continuum
pseudocritical temperature is determined. We have also extracted the continuum
limit of the total size of the system in both phases and for different
temperatures.Comment: Lattice 2000 (Gravity and Matrix Models
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