Wigner Oscillators, Twisted Hopf Algebras and Second Quantization

By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U^F(h) are shown to be induced from a more fundamental Hopf algebra obtained from the Schroedinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of the super-algebra osp(1|2n). We also discuss the possible implications in the context of quantum statistics.Comment: 23 page

(Re)Counting the poor in Peru: a multidimensional approach

After an impressive 12 point reduction in Peruvian monetary poverty, questions have been raised about the extent in which these figures mask deprivation in several other aspects critical for human development. We propose using the Alkire-Foster multidimensional headcount to address this issue, and devise a simple comparison framework to measure the tension between the incidence of monetary poverty and the overall level of deprivation based on the multidimensional measure. We select six dimensions and their respective indicators for the Peruvian case, and apply this framework using data for 2004 and 2008. Results indicate that we now face a larger risk of classifying as non-poor individuals who still endure significant deprivation if we rely on the conventional monetary dimension. In addition, inter and intraregional comparisons show that deprivations endured by the multidimensional poor are similar across regions and concentrated on the health and dwelling conditions dimensions, in particular, on the lack of adequate water and sanitation services. This last result reveals an opportunity to focalize public investment efforts.Multidimensional poverty; monetary poverty; Peru.

Brownian motion meets Riemann curvature

The general covariance of the diffusion equation is exploited in order to explore the curvature effects appearing on brownian motion over a d-dimensional curved manifold. We use the local frame defined by the so called Riemann normal coordinates to derive a general formula for the mean-square geodesic distance (MSD) at the short-time regime. This formula is written in terms of $O(d)$ invariants that depend on the Riemann curvature tensor. We study the n-dimensional sphere case to validate these results. We also show that the diffusion for positive constant curvature is slower than the diffusion in a plane space, while the diffusion for negative constant curvature turns out to be faster. Finally the two-dimensional case is emphasized, as it is relevant for the single particle diffusion on biomembranes.Comment: 16 pages and 3 figure

Coexistence of pressure-induced structural phases in bulk black phosphorus: a combined x-ray diffraction and Raman study up to 18 GPa

We report a study of the structural phase transitions induced by pressure in bulk black phosphorus by using both synchrotron x-ray diffraction for pressures up to 12.2 GPa and Raman spectroscopy up to 18.2 GPa. Very recently black phosphorus attracted large attention because of the unique properties of fewlayers samples (phosphorene), but some basic questions are still open in the case of the bulk system. As concerning the presence of a Raman spectrum above 10 GPa, which should not be observed in an elemental simple cubic system, we propose a new explanation by attributing a key role to the non-hydrostatic conditions occurring in Raman experiments. Finally, a combined analysis of Raman and XRD data allowed us to obtain quantitative information on presence and extent of coexistences between different structural phases from ~5 up to ~15 GPa. This information can have an important role in theoretical studies on pressure-induced structural and electronic phase transitions in black phosphorus