Observing gravitational lensing effects by Sgr A* with GRAVITY

The massive black hole at the Galactic center Sgr A* is surrounded by a cluster of stars orbiting around it. Light from these stars is bent by the gravitational field of the black hole, giving rise to several phenomena: astrometric displacement of the primary image, the creation of a secondary image that may shift the centroid of Sgr A*, magnification effects on both images. The near-to-come second generation VLTI instrument GRAVITY will perform observations in the Near Infrared of the Galactic Center at unprecedented resolution, opening the possibility of observing such effects. Here we investigate the observability limits for GRAVITY of gravitational lensing effects on the S-stars in the parameter space [DLS,gamma,K], where DLS is the distance between the lens and the source, gamma is the alignment angle of the source, and K is the source apparent magnitude in the K-band. The easiest effect to be observed in the next years is the astrometric displacement of primary images. In particular the shift of the star S17 from its Keplerian orbit will be detected as soon as GRAVITY becomes operative. For exceptional configurations it will be possible to detect effects related to the spin of the black hole or Post-Newtonian orders in the deflection.Comment: 29 pages, 9 figures, in press on Ap

Gravitational Lensing of stars in the central arcsecond of our Galaxy

In the neighborhood of Sgr A*, several stars (S2, S12, S14, S1, S8, S13) enjoy an accurate determination of their orbital parameters. General Relativity predicts that the central black hole acts as a gravitational lens on these stars, generating a secondary image and two infinite series of relativistic images. For each of these six stars, we calculate the light curves for the secondary and the first two relativistic images, in the Schwarzschild black hole hypothesis, throughout their orbital periods. The curves are peaked around the periapse epoch, but two subpeaks may arise in nearly edge-on orbits, when the source is behind or in front of Sgr A*. We show that for most of these stars the secondary image should be observable during its brightness peak. In particular, S14 is the best candidate, since its secondary image reaches K=23.3 with an angular separation of 0.125 mas from the apparent horizon of the central black hole. The detection of such images by future instruments could represent the first observation of gravitational lensing beyond the weak field approximation.Comment: 28 pages, 9 figures, in press on Ap

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10^8 - 10^9 solar masses in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.Comment: 8 pages, 3 figure

Deformed versus undeformed cat states encoding qubit

We study the possibility of exploiting superpositions of coherent states to encode qubit. A comparison between the use of deformed and undeformed bosonic algebra is made in connection with the amplitude damping errors.Comment: 6 pages, 2 eps figures, to appear in J. Opt.

The Hubbard model in the two-pole approximation

The two-dimensional Hubbard model is analyzed in the framework of the two-pole expansion. It is demonstrated that several theoretical approaches, when considered at their lowest level, are all equivalent and share the property of satisfying the conservation of the first four spectral momenta. It emerges that the various methods differ only in the way of fixing the internal parameters and that it exists a unique way to preserve simultaneously the Pauli principle and the particle-hole symmetry. A comprehensive comparison with respect to some general symmetry properties and the data from quantum Monte Carlo analysis shows the relevance of imposing the Pauli principle.Comment: 12 pages, 8 embedded Postscript figures, RevTeX, submitted to Int. Jou. Mod. Phys.

The Pauli Equation for Probability Distributions

The "marginal" distributions for measurable coordinate and spin projection is introduced. Then, the analog of the Pauli equation for spin-1/2 particle is obtained for such probability distributions instead of the usual wave functions. That allows a classical-like approach to quantum mechanics. Some illuminating examples are presented.Comment: 14 pages, ReVTe

Integração entre diferentes ferramentas de simulação.

A utilização de softwares para simulação algumas vezes encontra resistência, causada pela dificuldade de aprendizado e utilização da ferramenta, principalmente quando uma interface gráfica amigável não está disponível. No âmbito do projeto Pecus, utiliza-se o arcabouço MaCSim (MANCINI et al., 2013), no qual modelos matemáticos são codificados na linguagem de programação C++. O uso direto do arcabouço por especialistas de domínio, normalmente da área de ciências agrárias, é então dificultado pela necessidade de conhecimento de programação. Nesse contexto, desenvolveu-se ferramentas mais amigáveis para especificação de modelos que geram código para o arcabouço de simulação ou scripts em linguagem R. Uma vez que o MaCSim não possui interface gráfica, foi também desenvolvido um conjunto de classes na linguagem R para a entrada de dados, execução das simulações e visualização de resultados. Esse trabalho apresenta a integração dessas ferramentas no processo de desenvolvimento de simuladores do projeto PECUS

Beyond the Standard "Marginalizations" of Wigner Function

We discuss the problem of finding "marginal" distributions within different tomographic approaches to quantum state measurement, and we establish analytical connections among them.Comment: 12 pages, LaTex, no figures, to appear in Quantum and Semiclass. Op

Permutation symmetry for the tomographic probability distribution of a system of identical particles

The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution. Explicit calculations are performed in the case of the two-dimensional harmonic oscillator.Comment: 13 pages, latex, no figure