Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains

Integral identities for particular Bloch functions in finite periodic systems are derived. All following statements are proven for a finite domain consisting of an integer number of unit cells. It is shown that matrix elements of particular Bloch functions with respect to periodic differential operators vanish identically. The real valuedness, the time-independence and a summation property of the expectation values of periodic differential operators applied to superpositions of specific Bloch functions are derived.Comment: 10 page

Biperiodic superlattices and the transparent state

Coquelin et al. studied biperiodic semiconductor superlattices, which consist of alternating cell types, one with wide wells and the other narrow wells, separated by equal strength barriers. If the wells were identical, it would be a simply periodic system of $N = 2n$ half-cells. When asymmetry is introduced, an allowed band splits at the Bragg point into two disjoint allowed bands. The Bragg resonance turns into a transparent state located close to the band edge of the lower(upper) band when the first(second) well is the wider. Analysis of this system gives insight into how band splitting occurs. Further we consider semi-periodic systems having $N= 2n+1$ half-cells. Surprisingly these have very different transmission properties, with an envelope of maximum transmission probability that crosses the envelope of minima at the transparent point.Comment: 12 pages, 10 figures Version 2: improved figures using colour, and some small improvements in the text, in response to referee comments Version 3: incorporates changes which arose in proofs stag

Constructing a rational kinetic model of the selective propane oxidation over a mixed metal oxide catalyst

This research presents a kinetic investigation of the selective oxidation of propane to acrylic acid over a MoVTeNb oxide (M1 phase) catalyst. The paper contains both an overview of the related literature, and original results with a focus on kinetic aspects. Two types of kinetic experiments were performed in a plug flow reactor, observing (i) steady-state conditions (partial pressure variations) and (ii) the catalyst evolution as a function of time-on-stream. For this, the catalyst was treated in reducing atmosphere, before re-oxidising it. These observations in long term behaviour were used to distinguish different catalytic routes, namely for the formation of propene, acetic acid, acrylic acid, carbon monoxide and carbon dioxide. A partial carbon balance was introduced, which is a ‘kinetic fingerprint’, that distinguishes one type of active site from another. Furthermore, an ‘active site’ was found to consist of one or more ‘active centres’. A rational mechanism was developed based on the theory of graphs and includes two time scales belonging to (i) the catalytic cycle and (ii) the catalyst evolution. Several different types of active sites exist, at least as many, as kinetically independent product molecules are formed over a catalyst surface

Interminiband Rabi oscillations in biased semiconductor superlattices

Carrier dynamics at energy level anticrossings in biased semiconductor superlattices, was studied in the time domain by solving the time-dependent Schroedinger equation. The resonant nature of interminiband Rabi oscillations has been explicitly demonstrated to arise from interference of intrawell and Bloch oscillations. We also report a simulation of direct Rabi oscillations across three minibands, in the high field regime, due to interaction between three strongly coupled minibands.Comment: 13 pages, 16 figure

Electron transmission and phase time in semiconductor superlattices

We discuss the time spent by an electron propagating through a finite periodic system such as a semiconductor superlattice. The relation between dwell-time and phase-time is outlined. The envelopes of phase-time at maximum and minimum transmission are derived, and it is shown that the peaks and valleys of phase-time can be well described by parameters fitted at the extrema. For a many-period system this covers most of the allowed band. Comparison is made to direct numerical solutions of the time-dependent Schr\"odinger equation by Veenstra et al. [cond-mat/0411118] who compared systems with and without addition of an anti-reflection coating (ARC). With an ARC, the time delay is consistent with propagation at the Bloch velocity of the periodic system, which significantly reduces the time delay, in addition to increasing the transmissivity.Comment: 8 pages, 10 figures, based on a talk at Theory-Canada 3 in Edmonton AB, June 200

Simulation of Light Antinucleus-Nucleus Interactions

Creations of light anti-nuclei (anti-deuterium, anti-tritium, anti-He3 and anti-He4) are observed by collaborations at the LHC and RHIC accelerators. Some cosmic ray experiments are aimed to find the anti-nuclei in cosmic rays. To support the experimental studies of the anti-nuclei a Monte Carlo simulation of anti-nuclei interactions with matter is implemented in the Geant4 toolkit. The implementation combines practically all known theoretical approaches to the problem of antinucleon-nucleon interactions.Comment: 8 pages, 5 figure

Hour-glass magnetic excitations induced by nanoscopic phase separation in cobalt oxides La2−x_{2-x}Srx_xCoO4_4

The magnetic excitations in the cuprate superconductors might be essential for an understanding of high-temperature superconductivity. In these cuprate superconductors the magnetic excitation spectrum resembles an hour-glass and certain resonant magnetic excitations within are believed to be connected to the pairing mechanism which is corroborated by the observation of a universal linear scaling of superconducting gap and magnetic resonance energy. So far, charge stripes are widely believed to be involved in the physics of hour-glass spectra. Here we study an isostructural cobaltate that also exhibits an hour-glass magnetic spectrum. Instead of the expected charge stripe order we observe nano phase separation and unravel a microscopically split origin of hour-glass spectra on the nano scale pointing to a connection between the magnetic resonance peak and the spin gap originating in islands of the antiferromagnetic parent insulator. Our findings open new ways to theories of magnetic excitations and superconductivity in cuprate superconductors.Comment: Nature Communications 5, 5731 (2014

Pediatric surgical extracorporeal membrane oxygenation - a case series

Objective. To review demographic and procedural factors and their association with weaning rate and survival from extracorporeal membrane oxygenation (ECMO) in pediatric patients undergoing repair of cardiac malformations. Methods. The hospital records of children requiring ECMO during cardiac operation due to failure to wean from cardio-pulmonary by pass (CPB) were retrospectively reviewed, and an analysis of variables affecting survival was performed. Results. Thirty-five pediatric patients between January 1, 2000 and December 31, 2006 required ECMO for cardiopulmonary support during cardiac operations. ECMO survival was 54.3% and was comparable across all age groups. The lowest pH during ECMO treatment was the only predictor of mortality (P = 0.006). No other patient, surgical or anesthetic, factor was associated with either weaning from ECMO or hospital survival. Conclusions. No clear risk factor could be identified for survival from ECMO in our pediatric patients who underwent cardiac surgery and failed weaning from cardiopulmonary bypass