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

Efeito da caça no movimento e na área de uso dos jacarés, Pantanal Sul.

Na década de 80, a caça ilegal predominava no Pantanal, principalmente na área de rios, onde muitos jacarés foram mortos e suas carcaças encontradas em acampamentos dentro dos capões de mata. Caçadores mataram sete machos marcados que saíram da área de lagos para os rios. Na área de rios, as áreas usadas pelos cinco machos em locais não-sujeitos à caça. similares das usadas, pelos outros cinco machos em locais não -sujeitos à caça. O movimento de indivíduos de área não caçadas poe ser especialmente importante para o recrutamento de indivíduos à população em áreas caçadas, em longo prazo.bitstream/item/37293/1/BP61.pd

Quantum criticality as a resource for quantum estimation

We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and \lambda is the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order 1/L may be achieved in the estimation of \lambda at the critical point compared to the non-critical case. We show that analogue results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a specific exampl

Unpolarized light in quantum optics

We present a new derivation of the unpolarized quantum states of light, whose general form was first derived by Prakash and Chandra [Phys. Rev. A 4, 796 (1971)]. Our derivation makes use of some basic group theory, is straightforward, and offers some new insights.Comment: 3 pages, REVTeX, presented at ICQO'200

Determining R-parity violating parameters from neutrino and LHC data

In supersymmetric models neutrino data can be explained by R-parity violating operators which violate lepton number by one unit. The so called bilinear model can account for the observed neutrino data and predicts at the same time several decay properties of the lightest supersymmetric particle. In this paper we discuss the expected precision to determine these parameters by combining neutrino and LHC data and discuss the most important observables. We show that one can expect a rather accurate determination of the underlying R-parity parameters assuming mSUGRA relations between the R-parity conserving ones and discuss briefly also the general MSSM as well as the expected accuracies in case of a prospective e+ e- linear collider. An important observation is that several parameters can only be determined up to relative signs or more generally relative phases.Comment: 13 pages, 13 figure

Noncommutative Effects in the Black Hole Evaporation in Two Dimensions

We discuss some possible implications of a two-dimensional toy model for black hole evaporation in noncommutative field theory. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of massless and Hermitian scalar fields in the event horizon of a Schwarzschild black hole. We find that noncommutativity will affect the flux of outgoing particles and the nature of its UV/IR divergences. Moreover, we show that the noncommutative interaction does not affect Leahy's and Unruh's interpretation of thermal ingoing and outgoing fluxes in the black hole evaporation process. Thus, the noncommutative interaction still destroys the thermal nature of fluxes. In the process, some nonlocal implications of the noncommutativity are discussed.Comment: 33+1 pages, 3 eps figures, typos corrected, references added, figure 3 corrected, modifications in sections 4 and 6, version published in Phys. Rev.

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a ``non-perturbative'' behavior in some characteristic correlation lengths.Comment: 28 pages, RevTeX, no figure

Gravitational Lorentz Force and the Description of the Gravitational Interaction

In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analog of the Lorentz force. Then, we have shown that this force equation can be rewritten in terms of magnitudes related to either the teleparallel or the riemannian structures induced in spacetime by the presence of the gravitational field. In the first case, it gives a force equation, with torsion playing the role of force. In the second, it gives the usual geodesic equation of General Relativity. The main conclusion is that scalar matter is able to feel anyone of the above spacetime geometries, the teleparallel and the metric ones. Furthermore, both descriptions are found to be completely equivalent in the sense that they give the same physical trajectory for a spinless particle in a gravitational field.Comment: Equations (44)-(47) correcte