Manual of Quaternions

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Inelastic X-ray scattering from valence electrons near absorption edges of FeTe and TiSe2_2

We study resonant inelastic x-ray scattering (RIXS) peaks corresponding to low energy particle-hole excited states of metallic FeTe and semi-metallic TiSe$_2$ for photon incident energy tuned near the $L_{3}$ absorption edge of Fe and Ti respectively. We show that the cross section amplitudes are well described within a renormalization group theory where the effect of the core electrons is captured by effective dielectric functions expressed in terms of the the atomic scattering parameters $f_1$ of Fe and Ti. This method can be used to extract the dynamical structure factor from experimental RIXS spectra in metallic systems.Comment: 6 pages, 4 figure

Diffusion in pores and its dependence on boundary conditions

We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes. Partial slip is shown to significantly influence the diffusion coefficient near a wall. Analytical expressions are derived in the low and high confinement limits, and are in good agreement with numerical results. These calculations indicate that diffusion of tagged particles could be used as a sensitive probe of the solid-liquid boundary conditions.Comment: soumis \`a J.Phys. Cond. Matt. special issue on "Diffusion in Liquids, Polymers, Biophysics and Chemical Dynamics

Geometric optics and instability for semi-classical Schrodinger equations

We prove some instability phenomena for semi-classical (linear or) nonlinear Schrodinger equations. For some perturbations of the data, we show that for very small times, we can neglect the Laplacian, and the mechanism is the same as for the corresponding ordinary differential equation. Our approach allows smaller perturbations of the data, where the instability occurs for times such that the problem cannot be reduced to the study of an o.d.e.Comment: 22 pages. Corollary 1.7 adde

Hybrid-Entanglement in Continuous Variable Systems

Entanglement is one of the most fascinating features arising from quantum-mechanics and of great importance for quantum information science. Of particular interest are so-called hybrid-entangled states which have the intriguing property that they contain entanglement between different degrees of freedom (DOFs). However, most of the current continuous variable systems only exploit one DOF and therefore do not involve such highly complex states. We break this barrier and demonstrate that one can exploit squeezed cylindrically polarized optical modes to generate continuous variable states exhibiting entanglement between the spatial and polarization DOF. We show an experimental realization of these novel kind of states by quantum squeezing an azimuthally polarized mode with the help of a specially tailored photonic crystal fiber

High-level feature detection from video in TRECVid: a 5-year retrospective of achievements

Successful and effective content-based access to digital video requires fast, accurate and scalable methods to determine the video content automatically. A variety of contemporary approaches to this rely on text taken from speech within the video, or on matching one video frame against others using low-level characteristics like colour, texture, or shapes, or on determining and matching objects appearing within the video. Possibly the most important technique, however, is one which determines the presence or absence of a high-level or semantic feature, within a video clip or shot. By utilizing dozens, hundreds or even thousands of such semantic features we can support many kinds of content-based video navigation. Critically however, this depends on being able to determine whether each feature is or is not present in a video clip. The last 5 years have seen much progress in the development of techniques to determine the presence of semantic features within video. This progress can be tracked in the annual TRECVid benchmarking activity where dozens of research groups measure the effectiveness of their techniques on common data and using an open, metrics-based approach. In this chapter we summarise the work done on the TRECVid high-level feature task, showing the progress made year-on-year. This provides a fairly comprehensive statement on where the state-of-the-art is regarding this important task, not just for one research group or for one approach, but across the spectrum. We then use this past and on-going work as a basis for highlighting the trends that are emerging in this area, and the questions which remain to be addressed before we can achieve large-scale, fast and reliable high-level feature detection on video