Absolute continuity of the spectrum in a twisted Dirichlet-Neumann waveguide

International audienceQuantum waveguide with the shape of planar infinite straight strip and combined Dirichlet and Neumann boundary conditions on the opposite half-lines of the boundary is considered. The absence of the point as well as of the singular continuous spectrum is proved

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

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

Asymptotic behaviour of the spectrum of a waveguide with distant perturbations

We consider the waveguide modelled by a $n$-dimensional infinite tube. The operator we study is the Dirichlet Laplacian perturbed by two distant perturbations. The perturbations are described by arbitrary abstract operators ''localized'' in a certain sense, and the distance between their ''supports'' tends to infinity. We study the asymptotic behaviour of the discrete spectrum of such system. The main results are a convergence theorem and the asymptotics expansions for the eigenvalues. The asymptotic behaviour of the associated eigenfunctions is described as well. We also provide some particular examples of the distant perturbations. The examples are the potential, second order differential operator, magnetic Schroedinger operator, curved and deformed waveguide, delta interaction, and integral operator

SPI/INTEGRAL in-flight performance

The SPI instrument has been launched on-board the INTEGRAL observatory on October 17, 2002. SPI is a spectrometer devoted to the sky observation in the 20 keV-8 MeV energy range using 19 germanium detectors. The performance of the cryogenic system is nominal and allows to cool the 19 kg of germanium down to 85 K with a comfortable margin. The energy resolution of the whole camera is 2.5 keV at 1.1 MeV. This resolution degrades with time due to particle irradiation in space. We show that the annealing process allows the recovery of the initial performance. The anticoincidence shield works as expected, with a low threshold at 75 keV, reducing the GeD background by a factor of 20. The digital front-end electronics system allows the perfect alignement in time of all the signals as well as the optimisation of the dead time (12%). We demonstrate that SPI is able to map regions as complex as the galactic plane. The obtained spectrum of the Crab nebula validates the present version of our response matrix. The 3 $\sigma$ sensitivity of the instrument at 1 MeV is 8 10$^{-7}$ph$\cdot$cm$^{-2}\cdot$s$^{-1}\cdot$keV$^{-1}$ for the continuum and 3 10$^{-5}$ph$\cdot$cm$^{-2}\cdot$s$^{-1}$ for narrow lines.Comment: 10 pages, 18 figures, accepted for publication in A&A (special INTEGRAL volume

The Role of Climate Variability in the Spread of Malaria in Bangladeshi Highlands

Malaria is a major public health problem in Bangladesh, frequently occurring as epidemics since the 1990s. Many factors affect increases in malaria cases, including changes in land use, drug resistance, malaria control programs, socioeconomic issues, and climatic factors. No study has examined the relationship between malaria epidemics and climatic factors in Bangladesh. Here, we investigate the relationship between climatic parameters [rainfall, temperature, humidity, sea surface temperature (SST), El Niño-Southern Oscillation (ENSO), the normalized difference vegetation index (NDVI)], and malaria cases over the last 20 years in the malaria endemic district of Chittagong Hill Tracts (CHT)

ICAR: endoscopic skull‐base surgery

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