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

Free fermionic propagators on a lattice

A method used recently to obtain a formalism for classical fields with non-local actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens' principle with free discrete propagators that recover their continuum forms in certain limit.Comment: LaTex document, 13 pages, 1 figure. Minor changes, two references adde

MASS SEGREGATION IN DARK MATTER MODELS.

We use the moments of counts of neighbors as given by the Generalized Correlation Integrals, to study the clustering properties of Dark Matter Halos (DH) in Cold Dark Matter (CDM) and Cold+Hot Dark Matter (CHDM) models. We compare the results with those found in the CfA and SSRS galaxy catalogs. We show that if we apply the analysis in redshift space, both models reproduce equally well the observed clustering of galaxies. Mass segregation is also found in the models: more massive DHs are more clustered compared with less massive ones. In redshift space, this mass segregation is reduced by a factor 2-3 due to the peculiar velocities. Observational catalogs give an indication of luminosity and size segregation, which is consistent with the predictions of the models. Because the mass segregation is smaller in redshift space, it is suggestive that the real luminosity or size segregation of galaxies could be significantly larger than what it is found in redshift catalogs.Comment: 13 pages including 9 figures (220 KB) in uuencoded compressed Postscript format. To appear in The Astrophysical Journal, June 10. Latex file and figures available at ftp://astrohp.ft.uam.es/pub/preprints/masse

Large Scale Morphological Segregation in Optically Selected Galaxy Redshift Catalogs

We present the results of an exhaustive analysis of the morphological segregation of galaxies in the CfA and SSRS catalogs through the scaling formalism. Morphological segregation between ellipticals and spirals has been detected at scales up to 15-20 h$^{-1}$ Mpc in the CfA catalog, and up to 20-30 h$^{-1}$ Mpc in the SSRS catalog. Moreover, it is present not only in the densest areas of the galaxy distribution, but also in zones of moderate density.Comment: 9 pages, (1 figure included), uuencode compressed Postscript, (accepted for publication in ApJ Letters), FTUAM-93-2

Analytic Solutions to Coherent Control of the Dirac Equation

A simple framework for Dirac spinors is developed that parametrizes admissible quantum dynamics and also analytically constructs electromagnetic fields, obeying Maxwell's equations, which yield a desired evolution. In particular, we show how to achieve dispersionless rotation and translation of wave packets. Additionally, this formalism can handle control interactions beyond electromagnetic. This work reveals unexpected flexibility of the Dirac equation for control applications, which may open new prospects for quantum technologies

Dirac open quantum system dynamics: formulations and simulations

We present an open system interaction formalism for the Dirac equation. Overcoming a complexity bottleneck of alternative formulations, our framework enables efficient numerical simulations (utilizing a typical desktop) of relativistic dynamics within the von Neumann density matrix and Wigner phase space descriptions. Employing these instruments, we gain important insights into the effect of quantum dephasing for relativistic systems in many branches of physics. In particular, the conditions for robustness of Majorana spinors against dephasing are established. Using the Klein paradox and tunneling as examples, we show that quantum dephasing does not suppress negative energy particle generation. Hence, the Klein dynamics is also robust to dephasing