Classification of Energy Momentum Tensors in n≥5n \geq 5 Dimensional Space-times: a Review

Recent developments in string theory suggest that there might exist extra spatial dimensions, which are not small nor compact. The framework of a great number of brane cosmological models is that in which the matter fields are confined on a brane-world embedded in five dimensions (the bulk). Motivated by this we review the main results on the algebraic classification of second order symmetric tensors in 5-dimensional space-times. All possible Segre types for a symmetric two-tensor are found, and a set of canonical forms for each Segre type is obtained. A limiting diagram for the Segre types of these symmetric tensors in 5-D is built. Two theorems which collect together some basic results on the algebraic structure of second order symmetric tensors in 5-D are presented. We also show how one can obtain, by induction, the classification and the canonical forms of a symmetric two-tensor on n-dimensional (n > 5) spaces from its classification in 5-D spaces, present the Segre types in n-D and the corresponding canonical forms. This classification of symmetric two-tensors in any n-D spaces and their canonical forms are important in the context of n-dimensional brane-worlds context and also in the framework of 11-D supergravity and 10-D superstrings.Comment: LaTex2e, 18 pages. To appear in Braz.J.Phys (2004

Antiresonance and interaction-induced localization in spin and qubit chains with defects

We study a spin chain with an anisotropic XXZ coupling in an external field. Such a chain models several proposed types of a quantum computer. The chain contains a defect with a different on-site energy. The interaction between excitations is shown to lead to two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive quantum interference suppresses this decay. Numerical results confirm the analytical predictions.Comment: Updated versio

Vector constants of motion for time-dependent Kepler and isotropic harmonic oscillator potentials

A method of obtaining vector constants of motion for time-independent as well as time-dependent central fields is discussed. Some well-established results are rederived in this alternative way and new ones obtained.Comment: 18 pages, no figures, regular Latex article forma

The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle

In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when $\lambda$ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.Comment: 9 pages, no figures; version to appear in PLB. arXiv admin note: substantial text overlap with arXiv:1210.773