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

Is There a Euro Effect on Trade? An Application of End-of-Sample Structural Break Tests for Panel Data

Whether trade has increased due to the Euro is a question at the heart of lively policy debates and academic research. We revisit the question with a new, more powerful econometric test for end-of-sample breaks to formally identify the timing and duration of the structural break implied by the ÒRose effectÓ on the Euro AreaÕs trade. We find a significant break in 1999Q1 when using a traditional gravity equa- tion, corroborating the general consensus in the literature. However, we find that this break is short lived. Furthermore, we show that the break can be explained both by the marked decrease in real interest rates across the Euro Area and by deepening European institutional integration.Gravity equation, International Trade, Common Currency, Structural break tests in panel data, Euro Area

Security of two-way quantum cryptography against asymmetric Gaussian attacks

Recently, we have shown the advantages of two-way quantum communications in continuous variable quantum cryptography. Thanks to this new approach, two honest users can achieve a non-trivial security enhancement as long as the Gaussian interactions of an eavesdropper are independent and identical. In this work, we consider asymmetric strategies where the Gaussian interactions can be different and classically correlated. For several attacks of this kind, we prove that the enhancement of security still holds when the two-way protocols are used in direct reconciliation.Comment: Proceeding of the SPIE Conference "Quantum Communications and Quantum Imaging VI" - San Diego 2008. This paper is connected with arXiv:quant-ph/0611167 (for the last version see: Nature Physics 4, 726 (2008)

Quantum State Reconstruction of a Bose-Einstein Condensate

We propose a tomographic scheme to reconstruct the quantum state of a Bose-Einstein condensate, exploiting the radiation field as a probe and considering the atomic internal degrees of freedom. The density matrix in the number state basis can be directly retrieved from the atom counting probabilities.Comment: 11 pages, LaTeX file, no figures, to appear in Europhysics Letter

Confidential direct communications: a quantum approach using continuous variables

We consider the problem of privacy in direct communications, showing how quantum mechanics can be useful to guarantee a certain level of confidentiality. In particular, we review a continuous variable approach recently proposed by us [S. Pirandola et al., Europhys. Lett. 84, 20013 (2008)]. Here, we analyze the degree of privacy of this technique against a broader class of attacks, which includes non-Gaussian eavesdropping.Comment: Invited paper. Extension of results presented in arXiv:0802.0656 (REVTeX, 11 pages, 11 figures

Energy and technological refurbishment of the School of Architecture Valle Giulia, Rome

Modern architecture built in historical urban contexts represents a demanding issue when its energy efficiency should be improved. Indeed, the strongest efforts have to be made to maintain the architectural identity and its harmony with the surrounding cultural heritage. This study deals with the main building of the School of Architecture Valle Giulia in Rome, designed by Enrico Del Debbio in the 30’s. Further constraints are related to several interventions of airspace expansion starting from 1958 which involved the building starting from 1958. So, preservation would mean highlighting its historic change but, adapting the built environment to the contemporary users’ needs. As above-mentioned, the building belongs to the Valle delle Accademie, within the historic park of Villa Borghese, so that to acquire landscaping values. Those latter ones call for ulterior requirements when any new design process is conceived. The study provides a global renewal of the building accounting for the current low Indoor Environmental Quality in both summer and winter seasons and the lack of suitability to the contemporary University student’s needs. The interaction between building performance and HVAC systems was studied by collecting data and architectural surveys conducted by all the architects who modified the building. This procedure was chosen since thermo-physical investigations are considered destructive due to required perforations to identify the actual wall layers. Moreover, thermographic surveys were carried out to validate the modelled building response. The result of the study is the identification of viable interventions to improve the accessibility and fruition of the building as well as its energy performance. A specific cost-benefit analysis was done to prioritize the design options along with considering the measures needed to preserve all the architectural features and values

On Intergenerational Transmission of Reading Habits in Italy: Is a Good Example the Best Sermon?

The intergenerational transmission of preference and attitudes has been less investigated in the literature than the intergenerational transmission of education and income. Using the Italian Time Use Survey (2002-2003) conducted by ISTAT, we analyse the intergenerational transmission of reading habits: are children more likely to allocate time to studying and reading when they observe their parents doing the same activity? The intergeneration transmission of attitudes towards studying and reading can be explained by both cultural and educational transmission from parents to children and by imitating behaviours. The latter channel is of particular interest, since it entails a direct influence parents may have on child’s preference formation through their role model, and it opens the scope for active policies aimed at promoting good parents’ behaviours. We follow two fundamental approaches to estimation: a “long run” model, consisting of OLS intergenerational type regressions for the reading habit, and “short run” household fixed effect models, where we aim at identifying the impact of the role model exerted by parents, exploiting different exposure of sibling to parents’ example within the same household. Our long run results show that children are more likely to read and study when they live with parents that are used to read. Mothers seem to be more important than fathers in this type of intergenerational transmission. Moreover, the short run analysis shows that there is an imitation effect: in the day of the survey children are more likely to read after they saw either the mother or the father reading.