Indexed induction and coinduction, fibrationally.

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)

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

Unraveling the Nature of Charge Excitations in La2_2CuO4_4 with Momentum-Resolved Cu KK-edge Resonant Inelastic X-ray Scattering

Results of model calculations using exact diagonalization reveal the orbital character of states associated with different Raman loss peaks in Cu $K$-edge resonant inelastic X-ray scattering (RIXS) from La$_{2}$CuO$_{4}$. The model includes electronic orbitals necessary to highlight non-local Zhang-Rice singlet, charge transfer and $d$-$d$ excitations, as well as states with apical oxygen 2$p_z$ character. The dispersion of these excitations is discussed with prospects for resonant final state wave-function mapping. A good agreement with experiments emphasizes the substantial multi-orbital character of RIXS profiles in the energy transfer range 1-6 eV.Comment: Original: 4.5 pages. Replaced: 4 pages and 4 figures with updated content and reference

Quantum Mechanics Another Way

Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space take the place of operators, but the functions are multiplied in an exotic way, using the star product. Here we attempt a brief, pedagogical discussion of deformation quantization, that is suitable for inclusion in an undergraduate course.Comment: 14 pages, 3 figures, to be published in Eur. J. Phy

Adaptation to Antifaces and the Perception of Correct Famous Identity in an Average Face

Previous experiments have examined exposure to anti-identities (faces that possess traits opposite to an identity through a population average), finding that exposure to antifaces enhances recognition of the plus-identity images. Here we examine adaptation to antifaces using famous female celebrities. We demonstrate: that exposure to a color and shape transformed antiface of a celebrity increases the likelihood of perceiving the identity from which the antiface was manufactured in a composite face and that the effect shows size invariance (experiment 1), equivalent effects are seen in internet and laboratory-based studies (experiment 2), adaptation to shape-only antifaces has stronger effects on identity recognition than adaptation to color-only antifaces (experiment 3), and exposure to male versions of the antifaces does not influence the perception of female faces (experiment 4). Across these studies we found an effect of order where aftereffects were more pronounced in early than later trials. Overall, our studies delineate several aspects of identity aftereffects and support the proposal that identity is coded relative to other faces with special reference to a relatively sex-specific mean face representation

Pressure-tuning of the c-f hybridization in Yb metal detected by infrared spectroscopy up to 18 GPa

It has been known that the elemental Yb, a divalent metal at mbient pressure, becomes a mixed-valent metal under external pressure, with its valence reaching ~2.6 at 30 GPa. In this work, infrared spectroscopy has been used to probe the evolution of microscopic electronic states associated with the valence crossover in Yb at external pressures up to 18 GPa. The measured infrared reflectivity spectrum R(w) of Yb has shown large variations with pressure. In particular, R(w) develops a deep minimum in the mid-infrared, which shifts to lower energy with increasing pressure. The dip is attributed to optical absorption due to a conduction c-f electron hybridization state, similarly to those previously observed for heavy fermion compounds. The red shift of the dip indicates that the $c$-$f$ hybridization decreases with pressure, which is consistent with the increase of valence.Comment: 2 pages, to appear in J. Phys. Soc. Jpn. Supp