Scattering through a straight quantum waveguide with combined boundary conditions

Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered using stationary scattering theory. The existence of a matching conditions solution at x=0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.Comment: 26 pages, 3 figure

Diamagnetism of quantum gases with singular potentials

We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is jointly analytic in the chemical potential ant the intensity of the external magnetic field. We also discuss the thermodynamic limit

A century of warfare shoots holes in anti-Caulerpa campaign

Effort to have all varieties of the marine alga Caulerpa taxifolia listed as noxious weeds hinges on the argument that the alga's proliferation in the Mediterranean Sea is a cause and not a consequence of environmental degradation. Until now, the occurrence of two populations in a pristine part of the northern Mediterranean near the island of Porquerolles has upheld this claim. Here we show that the alga's development at Porquerolles is indeed a consequence of environmental degradation caused by military weapons' impacts on seagrass beds during the last century. The available data show that substratum enrichment plays a key role in fostering development of Caulerpa, irrespective of whether this results directly from pollution or from the impacts of pollution and other anthropogenic factors on benthic vegetation cover

Symmetry of bound and antibound states in the semiclassical limit

We consider one dimensional scattering and show how the presence of a mild positive barrier separating the interaction region from infinity implies that the bound and antibound states are symmetric modulo exponentially small errors in 1/h. This simple result was inspired by a numerical experiment and we describe the numerical scheme for an efficient computation of resonances in one dimension

Should We Assess Pituitary Function in Children After a Mild Traumatic Brain Injury? A Prospective Study

The aim of this study was to evaluate the frequency of hypopituitarism following TBI in a cohort of children who had been hospitalized for mild TBI and to identify the predictive factors for this deficiency. A prospective study was conducted on children between 2 and 16 years of age who had been hospitalized for mild TBI according to the Glasgow Coma Scale between September 2009 and June 2013. Clinical parameters, basal pituitary hormone assessment at 0, 6, and 12 months, as well as a dynamic testing (insulin tolerance test) 12 months after TBI were performed. The study included 109 children, the median age was 8.5 years. Patients were examined 6 months ( = 99) and 12 months ( = 96) after TBI. Somatotropic deficiency (defined by a GH peak <20 mUI/l in two tests, an IGF-1 <-1SDS and a delta height <0SDS) were confirmed in 2 cases. One case of gonadotrophic deficiency occurred 1 year after TBI among 13 pubertal children. No cases of precocious puberty, 5 cases of low prolactin level, no cases of corticotropic insufficiency (cortisol peak <500 nmol/l) and no cases diabetes insipidus were recorded. Pituitary insufficiency was present 1year after mild TBI in about 7% of children. Based on our results, we suggest testing children after mild TBI in case of clinical abnormalities. i.e., for GH axis, IGF-1, which should be assessed in children with a delta height <0 SDS, 6 to 12 months after TBI, and a dynamic GH testing (preferentially by an ITT) should be performed in case of IGF-1 <-1SDS, with a GH threshold at 20 mUI/L. However, if a systematic pituitary assessment is not required for mild TBI, physicians should monitor children 1 year after mild TBI with particular attention to growth and weight gain

Exponential splitting of bound states in a waveguide with a pair of distant windows

We consider Laplacian in a straight planar strip with Dirichlet boundary which has two Neumann ``windows'' of the same length the centers of which are $2l$ apart, and study the asymptotic behaviour of the discrete spectrum as $l\to\infty$. It is shown that there are pairs of eigenvalues around each isolated eigenvalue of a single-window strip and their distances vanish exponentially in the limit $l\to\infty$. We derive an asymptotic expansion also in the case where a single window gives rise to a threshold resonance which the presence of the other window turns into a single isolated eigenvalue

Spectral flow and level spacing of edge states for quantum Hall hamiltonians

We consider a non relativistic particle on the surface of a semi-infinite cylinder of circumference $L$ submitted to a perpendicular magnetic field of strength $B$ and to the potential of impurities of maximal amplitude $w$. This model is of importance in the context of the integer quantum Hall effect. In the regime of strong magnetic field or weak disorder $B>>w$ it is known that there are chiral edge states, which are localised within a few magnetic lengths close to, and extended along the boundary of the cylinder, and whose energy levels lie in the gaps of the bulk system. These energy levels have a spectral flow, uniform in $L$, as a function of a magnetic flux which threads the cylinder along its axis. Through a detailed study of this spectral flow we prove that the spacing between two consecutive levels of edge states is bounded below by $2\pi\alpha L^{-1}$ with $\alpha>0$, independent of $L$, and of the configuration of impurities. This implies that the level repulsion of the chiral edge states is much stronger than that of extended states in the usual Anderson model and their statistics cannot obey one of the Gaussian ensembles. Our analysis uses the notion of relative index between two projections and indicates that the level repulsion is connected to topological aspects of quantum Hall systems.Comment: 22 pages, no figure

On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page

Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur

Impact of cyclosporine dosing regimen and infection on voriconazole pharmacodynamics in an experimental model of cerebral scedosporiosis

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