Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems

Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space dynamics in their neighborhood. We provide a pedestrian presentation of this classical theory and extend it by including systematically the periodic orbits lying in the complex plane on each side of the bifurcation. This allows for a more coherent and unified treatment of contributions of periodic orbits in semiclassical expansions. The contribution of complex fixed points is find to be exponentially small only for a particular type of bifurcation (the extremal one). In all other cases complex orbits give rise to corrections in powers of $\hbar$ and, unlike the former one, their contribution is hidden in the ``shadow'' of a real periodic orbit.Comment: better ps figures available at http://www.phys.univ-tours.fr/~mouchet or on request to [email protected]

Influence of classical resonances on chaotic tunnelling

Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular phase-space islands on which the stable modes are localized. By means of a quantitative numerical study of the corresponding Floquet problem, we identify the trace of such resonances not only in the level splittings between near-degenerate quantum states, where they lead to prominent plateau structures, but also in overlap matrix elements of the Floquet eigenstates, which reveal characteristic sequences of avoided crossings in the Floquet spectrum. The semiclassical theory of resonance-assisted tunnelling yields good overall agreement with the quantum-tunnelling rates, and indicates that partial barriers within the chaos might play a prominent role

Impact de pulvérisations de deltaméthrine dans un foyer de leishmaniose de Bolivie

Une unique pulvérisation domiciliaire de K-Othrine à 0,025 g/m2, en début de saison humide, contrôle efficacement les populations domestiques et péridomestiques de #Lutzomyia longipalpis, le vecteur de la leishmaniose viscérale, dans un village submontagnard de la province Nord-Yungas, Bolivie. Ce phlébotome est éliminé des habitations et des poulaillers durant, respectivement, 9 et 10 mois. Par contre, l'impact des traitements sur #Lu. nuneztovari anglesi, le vecteur présumé de la leishmaniose tégumentaire, est beaucoup moins marqué. Il se traduit, plus par une baisse de 50 % du taux de gorgement des populations capturées dans les maisons, que par une diminution de leur densité, difficile à apprécier du fait des variations saisonnières naturelles, et de l'absence de témoin représentatif. Ce résultat n'est pas inattendu, étant donné la forte exophilie de #Lu. n. anglesi$ dans la région. (Résumé d'auteur