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

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

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

'Nature or nurture': survival rate oviposition interval, and possible gonotrophic discordance among South East Asian anophelines

Background: Mosquito survival, oviposition interval and gonotrophic concordance are important determinants of vectorial capacity. These may vary between species or within a single species depending on the environment. They may be estimated by examination of the ovaries of host-seeking mosquitoes. Methods: Landing collections, Furvela tent-trap and CDC light-trap collections were undertaken sequentially in four locations in Cambodia between February 2012 and December 2013 and samples from the collected mosquitoes were dissected to determine parity, sac stage (indicative of time spent prior to returning to feed) and egg stage. Results: A total of 27,876 Anopheles from 15 species or species groups were collected in the four locations and 2883 specimens were dissected. Both the density and predominant species collected varied according to location and trapping method. Five species were dissected in sufficient numbers to allow comparisons between locations. Estimated oviposition interval differed markedly between species but less within species among different locations. Anopheles aconitus had the shortest cycle, which was 3.17 days (95 % CI 3–3.64), and Anopheles barbirostris had the longest cycle, which took four days (95 % CI 3.29–4). Anopheles minimus had a higher sac rate in weeks leading up to a full moon but there was apparently little effect of moon phase on Anopheles dirus. Despite the fact that many of the species occurred at very low densities, there was no evidence of gonotrophic dissociation in any of them, even during sustained hot, dry periods. The principal Cambodian malaria vector, An. dirus, was only common in one location where it was collected in miniature light-traps inside houses. It did not appear to have an exceptional survival rate (as judged by the low average parous rate) or oviposition cycle. Conclusions: Differences in the oviposition interval were more pronounced among species within locations than within species among ecologically diverse locations. A nationwide survey using CDC light-traps for the collection of An. dirus inside houses may help in determining patterns of malaria transmission in Cambodia

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

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

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

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