On Koopman-von Neumann Waves II

In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the introduction of the KvN Hilbert space of complex and square integrable "wave functions" requires an enlargement of the set of the observables of ordinary classical mechanics. The possible role and the meaning of these extra observables is briefly indicated in this work. We also analyze the similarities and differences between non selective measurements and two-slit experiments in classical and quantum mechanics.Comment: 18+1 pages, 1 figure, misprints fixe

Quantum error correction with degenerate codes for correlated noise

We introduce a quantum packing bound on the minimal resources required by nondegenerate error correction codes for any kind of noise. We prove that degenerate codes can outperform nondegenerate ones in the presence of correlated noise, by exhibiting examples where the quantum packing bound is violated.Comment: 5 pages, published versio

Wavevector Selective Metasurfaces and Tunnel Vision Filters

Metasurfaces offer unprecedented flexibility in the design and control of light propagation, replacing bulk optical components and exhibiting exotic optical effects. One of the basic properties of the metasurfaces, which renders them as frequency selective surfaces, is the ability to transmit or reflect radiation within a narrow spectral band that can be engineered on demand. Here we introduce and demonstrate experimentally in the THz domain the concept of wavevector selective surfaces -- metasurfaces transparent only within a narrow range of light propagation directions operating effectively as tunnel vision filters. Practical implementations of the new concept include applications in wavefront manipulation, observational instruments, vision and free-space communication in light-scattering environments, as well as passive camouflage

The peculiar Na-O anticorrelation of the bulge globular cluster NGC 6440

Context. Galactic Globular Clusters (GCs) are essential tools to understand the earliest epoch of the Milky Way, since they are among the oldest objects in the Universe and can be used to trace its formation and evolution. Current studies using high resolution spectroscopy for many stars in each of a large sample of GCs allow us to develop a detailed observational picture about their formation and their relation with the Galaxy. However, it is necessary to complete this picture by including GCs that belong to all major Galactic components, including the Bulge. Aims. Our aim is to perform a detailed chemical analyses of the bulge GC NGC 6440 in order to determine if this object has Multiple Populations (MPs) and investigate its relation with the Bulge of the Milky Way and with the other Galactic GCs, especially those associated with the Bulge, which are largely poorly studied. Methods. We determined the stellar parameters and the chemical abundances of light elements (Na, Al), iron-peak elements (Fe, Sc, Mn, Co, Ni), $\alpha$-elements (O, Mg, Si, Ca, Ti) and heavy elements (Ba, Eu) in seven red giant members of NGC 6440 using high resolution spectroscopy from FLAMES@UVES. Results. We found a mean iron content of [Fe/H]=-0.50$\pm$0.03 dex in agreement with other studies. We found no internal iron spread. On the other hand, Na and Al show a significant intrinsic spread, but the cluster has no significant O-Na anticorrelation nor exhibits a Mg-Al anticorrelation. The $\alpha$-elements show good agreement with the Bulge field star trend, although they are at the high alpha end and are also higher than those of other GCs of comparable metallicity. The heavy elements are dominated by the r-process, indicating a strong contribution by SNeII. The chemical analysis suggests an origin similar to that of the Bulge field stars.Comment: 12 pages, 13 figures, Accepted for publication in A&

Optimal estimation of quantum observables

We consider the problem of estimating the ensemble average of an observable on an ensemble of equally prepared identical quantum systems. We show that, among all kinds of measurements performed jointly on the copies, the optimal unbiased estimation is achieved by the usual procedure that consists in performing independent measurements of the observable on each system and averaging the measurement outcomes.Comment: Submitted to J. Math Phy

Milage aprender+ uma app para aprender matemática usando smartphones e tablets

O baixo desempenho dos estudantes na aprendizagem da matemática constitui problema que em alguns países se tem vindo a acentuar nos últimos anos. De acordo com um estudo realizado pelo Departamento de Educação dos EUA, em 2010, as aulas em regime de blended-learning, ou b-learning, apresentam melhores resultados do que as tradicionais aulas presenciais. Por outro lado, observa-se um número crescente de estudantes que usa smartphones e tablets nas escolas, cuja popularidade pode ser aproveitada para estimular a sua utilização em atividades educacionais para melhorar a aprendizagem. Nesta comunicação apresenta-se uma nova aplicação para dispositivos móveis, smartphones e tablets, app MILAGE, através da qual o aluno pode aceder a conteúdos pedagógicos, dentro e fora da sala de aula. De modo a estimular e apoiar a realização das várias atividades propostas, a interface incorpora características de gamificação e recursos multimédia.info:eu-repo/semantics/publishedVersio

Vanishing of the upper critical field in Bi_2Sr_2CaCu_2O_{8+\delta} from Landau-Ott scaling

We apply Landau-Ott scaling to the reversible magnetization data of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ published by Y. Wang et al. [\emph{Phys. Rev. Lett. \textbf{95} 247002 (2005)}] and find that the extrapolation of the Landau-Ott upper critical field line vanishes at a critical temperature parameter, T^*_c, a few degrees above the zero resistivity critical temperature, T_c. Only isothermal curves below and near to T_c were used to determine this transition temperature. This temperature is associated to the disappearance of the mixed state instead of a complete suppression of superconductivity in the sample.Comment: 3 figure

The Beta coefficient of an unlisted bank

The problem that we set ourselves in this work is related to the determination of capital return invested in an unlisted bank, particularly, in a credit cooperative bank. The model that we use is the Capital Asset Pricing Model (CAPM) equation, with its various difficulties in applying it to a category of unlisted activities. The biggest obstacle in using CAPM is given by the Beta determination representing the systematic risk of the units under examination. Therefore, to determine this risk coefficient, we assumed a first step in which we consider a similar sector sample, consists of a portfolio of listed banks, from which we obtain a Business Risk Index (BRI), that we use to go back to unlisted bank Beta under consideration. In a second case, it is thought of a target market constituted by the whole unlisted banks sample of the same sector under analysis, then relating the returns of individual observed banks with average returns provided by this market, we obtain the Regression Beta. A third step, provides the Business Risk Index determination of the sector, in this case obtained from the unlisted banks market, and then to reach to our banks Beta under observation. Comparing the results obtained from this analysis allows us to suggest a quite satisfying line for determining the Beta of an unlisted bank and consequently for its expected return estimation

Extremal covariant measurements

We characterize the extremal points of the convex set of quantum measurements that are covariant under a finite-dimensional projective representation of a compact group, with action of the group on the measurement probability space which is generally non-transitive. In this case the POVM density is made of multiple orbits of positive operators, and, in the case of extremal measurements, we provide a bound for the number of orbits and for the rank of POVM elements. Two relevant applications are considered, concerning state discrimination with mutually unbiased bases and the maximization of the mutual information.Comment: 11 pages, no figure