Exact propagators on the lattice with applications to diffractive effects

The propagator of the discrete Schr\"odinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are studied analytically by the application of the new propagator. In the second part of this paper, the analogy between time propagation and 2D scattering by 1D obstacles is explored. New results are given in the context of diffraction by edges within a periodic medium. A connection with tight-binding arrays and photonic crystals is indicated.Comment: Final version with two appendices. Published in J. Phys. A: Math. Theo

Decoherence at constant excitation

We present a simple exactly solvable extension of of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of $4\times 4$ matrices

Relativistic echo dynamics and the stability of a beam of Landau electrons

We extend the concepts of echo dynamics and fidelity decay to relativistic quantum mechanics, specifically in the context of Klein-Gordon and Dirac equations under external electromagnetic fields. In both cases we define similar expressions for the fidelity amplitude under perturbations of these fields, and a covariant version of the echo operator. Transformation properties under the Lorentz group are established. An alternate expression for fidelity is given in the Dirac case in terms of a 4-current. As an application we study a beam of Landau electrons perturbed by field inhomogeneities.Comment: 8 pages, no figure

Phase Space Evolution and Discontinuous Schr\"odinger Waves

The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous wavepackets, generating expansions similar to those of wavelet analysis. Such transformations are identified as the cause for the infinitesimal details in diffraction patterns. A simple case of an evolution map, such as SL(2) in a two-dimensional phase space, is shown to produce an infinite set of space-time trajectories of constant probability. The trajectories emerge from a breaking point of the initial wave.Comment: Presented at the conference QTS7, Prague 2011. 12 pages, 7 figure

Playing relativistic billiards beyond graphene

The possibility of using hexagonal structures in general and graphene in particular to emulate the Dirac equation is the basis of our considerations. We show that Dirac oscillators with or without restmass can be emulated by distorting a tight binding model on a hexagonal structure. In a quest to make a toy model for such relativistic equations we first show that a hexagonal lattice of attractive potential wells would be a good candidate. First we consider the corresponding one-dimensional model giving rise to a one-dimensional Dirac oscillator, and then construct explicitly the deformations needed in the two-dimensional case. Finally we discuss, how such a model can be implemented as an electromagnetic billiard using arrays of dielectric resonators between two conducting plates that ensure evanescent modes outside the resonators for transversal electric modes, and describe an appropriate experimental setup.Comment: 23 pages, 8 figures. Submitted to NJ

Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and and their relative behaviour in the concurrence-purity plane.Comment: 10 pages, 3 figure

Impact of Dietary Supplementation with Sodium Butyrate Protected by Medium-Chain Fatty Acid Salts on Gut Health of Broiler Chickens

This research was co-funded by the European Fund of Regional Development of the European Union within the framework of the FEDER operating program of Catalunya 2014-2020 (project COMRDI16-1-0033) and managed by ACCIÓ.Nutritional strategies to improve gut health of broilers are under research. This study investigated the effect of dietary supplementation with sodium butyrate protected by sodium salts of medium-chain fatty acids as a feed additive on broiler gut health. The first experiment was conducted to evaluate the effect of supplementing at 0.5, 1, and 2 kg/t in broilers housed under optimal conditions. Supplementation at 0.5 and 1 kg/t maintained goblet cell counts at 10 days of age (p ≤ 0.05), and supplementation at 1 kg/t decreased intraepithelial lymphocyte counts compared to 2 kg/t at 39 days (p ≤ 0.10). Abdominal fat pad levels of lauric and myristic acids were gradually increased by supplement dose (p ≤ 0.05). In the second experiment, the feed additive at 1 kg/t was evaluated in coccidiosis-challenged broilers. Experimental treatments were as follows: non-challenged, control-challenged, and supplemented-challenged treatments. Coccidiosis negatively impact performance and modify histomorphometry and microbiota (p ≤ 0.05). The feed additive increased crypt depth at 7 days post-inoculation and goblet cell count at 14 days post-inoculation (p ≤ 0.05). Further, supplementation interacted with the microbiota modification led by the coccidiosis (p ≤ 0.05). These results suggest that this feed additive could be a useful strategy to reinforce the gut barrier, especially for birds under coccidiosis-challenge treatments

Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem

A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators

Obstetric complications and clinical presentation in first episode of psychosis

Objective: Psychotic disorders exhibit a complex aetiology that combines genetic and environmental factors. Among the latter, obstetric complications (OCs) have been widely studied as risk factors, but it is not yet well understood how OCs relate to the heterogeneous presentations of psychotic disorders. We assessed the clinical phenotypes of individuals with a first episode of psychosis (FEP) in relation to the presence of OCs. Methods: Two-hundred seventy-seven patients with an FEP were assessed for OCs using the Lewis–Murray scale, with data stratified into three subscales depending on the timing and the characteristics of the obstetric event, namely: complications of pregnancy, abnormal foetal growth and development and difficulties in delivery. We also considered other two groups: any complications during the pregnancy period and all OCs taken altogether. Patients were clinically evaluated with the Positive and Negative Syndrome Scale for schizophrenia. Results: Total OCs and difficulties in delivery were related to more severe psychopathology, and this remained significant after co-varying for age, sex, traumatic experiences, antipsychotic dosage and cannabis use. Conclusions: Our results highlight the relevance of OCs for the clinical presentation of psychosis. Describing the timing of the OCs is essential in understanding the heterogeneity of the clinical presentation