Clustering statistics in cosmology

The main tools in cosmology for comparing theoretical models with the observations of the galaxy distribution are statistical. We will review the applications of spatial statistics to the description of the large-scale structure of the universe. Special topics discussed in this talk will be: description of the galaxy samples, selection effects and biases, correlation functions, Fourier analysis, nearest neighbor statistics, Minkowski functionals and structure statistics. Special attention will be devoted to scaling laws and the use of the lacunarity measures in the description of the cosmic texture.Comment: 15 pages, 7 figures, uses spie.cls (included). This paper will be published in SPIE Proceedings Vol. 4847, 2002, "Astronomical Data Analysis II," J.-L. Stark and F. Murtagh, eds., and is made available as an electronic preprint with permission of SPI

Vortex-glass transition in superconducting Nb/Cu superlattices

Nb/Cu superconducting superlattices have been fabricated by dc magnetron sputtering. This system shows a vortex glass transition with critical exponents similar to high temperatures superconductors exponents. The transition dymensionality is governed by the superconducting coupling regime. The vortex glass transition shows a pure two dimensional behavior in decoupled superlattices and a quasi-two dimensional behavior in the superlattice coupling regime.Comment: 9 pages, 3 figure

Geometric approach to non-relativistic Quantum Dynamics of mixed states

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the projection of the geodesic flow to the base manifold gives the temporal evolution predicted by the von Neumann equation. Using that approach we can describe every conserved quantum observable as a Killing vector field, and provide a geometric proof for the Poincare quantum recurrence in a physical system with finite energy levels.Comment: 19 pages, 1 figure. Minor corrections. Accepted to Journal of Mathematical Physic