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

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

Nectar ecology of the endemic epiphytic hummingbird-pollinated bromeliad Vriesea altodaserrae: secretion dynamics and pollinator visitation pattern

Hummingbirds are the main pollinators of most bromeliad species, whose nectar traits usually respond to the selective pressures imposed by pollinators. Considering the specialization of hummingbird-pollinated bromeliads, we expect a close relationship between nectar ecophysiology and the needs of the main pollinators. In this sense, we studied the nectar ecology of the endemic epiphytic bromeliad Vriesea altodaserrae by assessing its nectar traits to address the following questions: i) do flowers respond to successive experimental removals of nectar? ii) is hummingbird visitation frequency related to nectar secretion pattern? We found that V. altodaserrae depended completely on hummingbirds for sexual reproduction, and nectar composition was consistent with that of most hummingbird-pollinated species. Most of the nectar was secreted at bud stage and, if not removed, flowers reabsorb it at the end of their lifespan. Total nectar production did not change after successive removals, and nectar secretion rhythm did not affect the frequency of hummingbird visits. Vriesea altodaserrae was visited by two-thirds of the hummingbird species recorded at the study site, but especially by those of Trochilinae subfamily, suggesting specialization for this group of hummingbirds and highlighting the importance this endemic bromeliad as a keystone species in areas of highland Atlantic fores

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

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

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 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

Expert opinion on pituitary complications in immunotherapy

Hypophysitis is a frequent toxic endocrine side-effect of immunotherapy. Prevalence is higher with anti-CTLA-4 antibodies (4-20%) or in association with PD-1 inhibitors (8%). Diagnosis is presumptive, based on poorly specific clinical symptoms (usually, headache and asthenia) and/or hyponatremia and/or at least one pituitary deficit and/or abnormal imaging. Visual disorder or polyuropolydipsic syndrome are exceptional. In decreasing order of frequency, deficits are thyrotropic (86-100%), gonadotropic (85-100%) or corticotropic (50-73%); somatotropin deficit or abnormal prolactin level are rarer. Pituitary MRI in acute phase shows variable moderate increase in pituitary volume, ruling out differential diagnoses, especially pituitary metastasis. Treatment of corticotropin deficiency requires systematic emergency replacement therapy, with the usual modalities, while treatment of other deficits depends on clinical status and progression. Thyrotropin and gonadotropin deficits usually recover, but corticotropin deficiency persists over the long term, requiring education and specialized endocrinologic follow-up. Onset of hypophysitis does not contraindicate continuation of immunotherapy and does not usually require high dose synthetic glucocorticoids

Implementing an Advanced Laparoscopic Procedure by Monitoring with a Visiting Surgeon

Study Objective: To investigate the feasibility of safely implementing a total laparoscopic hysterectomy (LH) in established gynecologists' practices with on-site coaching and monitoring of the learning curve by an experienced visiting surgeon. Design: Multicenter prospective feasibility and implementation study (Canadian Task Force classification II-2). Setting: Eleven general gynecologists in 8 hospitals (1 university hospital and 7 regional hospitals) participated. Patients: Laparoscopic hysterectomy was performed in 83 patients during the learning curve, and in 83 patients after the learning curve. Interventions: During the learning curve, an experienced visiting laparoscopist was available for coaching during each LH. A competence score was marked on an Objective Structured Assessment of Technical Skills (OSATS) form. Complications were recorded intraoperatively and postoperatively for 6 weeks after surgery in all patients. Measurements and Main Results: Nine of 11 gynecologists reached the competence score of at least 28 points during the study, from January 2005 to January 2007. A major complication occurred in 3 of 83 LH procedures (4%) performed during the learning curve, and in 5 of 83 LH procedures (6%) performed after the learning curve (p = .72). Conclusion: The concept of a visiting surgeon for on-site coaching and monitoring of established gynecologists during the learning curve of an advanced laparoscopic procedure using Objectively Structured Assessment of Technical Skills is feasible. According to the observed complication rate during and after the learning curve, on-site coaching is a useful tool when implementing a new laparoscopic technique in established gynecologists' practices. Journal of Minimally Invasive Gynecology (2010) 17, 771-778 (C) 2010 AAGL. All rights reserved

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure