Understanding interference experiments with polarized light through photon trajectories

Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago-Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago-Fresnel laws for the interference of polarized light.Comment: 36 pages, 6 figure

Should particle trajectories comply with the transverse momentum distribution?

The momentum distributions associated with both the wave function of a particle behind a grating and the corresponding Bohmian trajectories are investigated and compared. Near the grating, it is observed that the former does not depend on the distance from the grating, while the latter changes with this distance. However, as one moves further apart from the grating, in the far field, both distributions become identical.Comment: 10 pages, 7 figure

Generalization of Vélu's formulae

Given an elliptic curve $E$ and a finite subgroup $G$, Vélu's formulae concern to a separable isogeny $\mathcal{I}_G\colon E\to E'$ with kernel $G$. In particular, for a point $P\in E$ these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set $P+G$ as the difference between the abscissa of $\mathcal{I}_G(P)$ and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel $G$. On the other hand, they express Weierstrass coefficients of $E'$ as polynomials in the coefficients of $E$ and two additional parameters: $w_0=t$ and $w_1=w$. We generalize this by defining parameters $w_n$ for all $n\ge 0$ and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in $P+G$. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when $G$ is a rational group

The electron-phonon coupling strength at metal surfaces directly determined from the Helium atom scattering Debye-Waller factor

A new quantum-theoretical derivation of the elastic and inelastic scattering probability of He atoms from a metal surface, where the energy and momentum exchange with the phonon gas can only occur through the mediation of the surface free-electron density, shows that the Debye-Waller exponent is directly proportional to the electron-phonon mass coupling constant $\lambda$. The comparison between the values of $\lambda$ extracted from existing data on the Debye-Waller factor for various metal surfaces and the $\lambda$ values known from literature indicates a substantial agreement, which opens the possibility of directly extracting the electron-phonon coupling strength in quasi-2D conducting systems from the temperature or incident energy dependence of the elastic Helium atom scattering intensities.Comment: 14 pages, 2 figures, 1 tabl

La Biblioteca de la Memoria

La Biblioteca de la Memòria és un projecte de la Biblioteca Central d'Igualadaque es presenta com una experiència de cerca, recollida, conservació i divulgació de testimonis personals duta a terme per la biblioteca pública. Com a característiques principals cal remarcar-ne la implicació d'entitats i persones en aquesta idea comuna de promoure la cerca i de recollir testimonis de memòria popular. Se n'explica la metodologia i els resultats, de manera que pugui servir com a pauta de treball per a d'altres biblioteques públiques que vulguin endegar projectes semblants per tal de preservar la història oral de Catalunya.The Library of Memory is a project of the Central Library of Igualada. Described is this public library’s experience in searching for, collecting, conserving and disseminating personal testimony. One of the key features has been the involvement of both organisations and individuals in this  communal idea to encourage that memories of townspeople be sought out and gathered. The fact that the project has been organised by a public library may encourage other libraries to carry out similar projects. Given the size and integration among the inhabitants of the Catalan library network, collecting  oral history is seen as an important task that it can perform.La Biblioteca de la Memòria es un proyecto de la Biblioteca Central d’Igualada que se presenta como una experiencia de búsqueda, recopilación, conservación y divulgación de testimonios personales, llevada a cabo por la biblioteca pública. Como características principales hay que remarcar la implicación de entidades y personas en esta idea, con el fin de promover la búsqueda y recoger testimonios de memoria popular. Se explica la metodología de trabajo y los resultados, de forma que puedan servir como pauta para otras bibliotecas públicas interesadas en iniciar proyectos similares, contribuyendo así a la preservación de la historia oral de Cataluña

Oblique surface waves at an interface of metal-dielectric superlattice and isotropic dielectric

We investigate the existence and the dispersion characteristics of surface waves that propagate at an interface between metal-dielectric superlattice and isotropic dielectric. Within the long wavelength limit, when the effective-medium approximation is valid, the superlattice behaves like a uniaxial plasmonic crystal with the main optical axes perpendicular to the metal-dielectric interfaces. We demonstrate that if such a semi-infinite plasmonic crystal is cut normally to the layer interfaces and brought into the contact with semi-infinite dielectric, a new type of surface modes can appear. The propagation of such modes obliquely to the optical axes occurs under favorable conditions that regard thicknesses of the layers, as well as the proper choice of dielectric permittivity of the constituent materials. We show that losses within the metallic layers can be substantially reduced by making the layers sufficiently thin. At the same time, a dramatic enlargement of the range of angles for oblique propagation of the new surface modes is observed. This can lead, however, to the field non-locality and consequently to the failure of the effective-medium approximation.Comment: 4 pages, 3 figure

Familias de curvas elípticas adecuadas para Criptografía Basada en la Identidad

La Criptografía Basada en la Identidad hace uso de curvas elípticas que satisfacen ciertas condiciones (pairingfriendly curves), en particular, el grado de inmersión de dichas curvas debe ser pequeño. En este trabajo se obtienen familias explicitas de curvas elípticas idóneas para este escenario. Dicha criptografía está basada en el cálculo de emparejamientos sobre curvas, cálculo factible gracias al algoritmo de Miller. Proponemos una versión más eficiente que la clásica de este algoritmo usando la representación de un número en forma no adyacente (NAF).Este trabajo ha sido financiado por el Ministerio de Economía y Competitividad con los proyectos MTM2010-21580-C02-01/02 y MTM2010-16051