Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics

Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed for the corresponding Borel functions. Its main property is to order the singularity structure of the Borel plane in a hierarchical way by an increasing complexity of this structure starting from the analytic one. This allows us to study the Borel plane singularity structure in a systematic way. Examples of such structures are considered for linear, harmonic and anharmonic potentials. Together with the best approximation provided by the semiclassical series the exponentially small contribution completing the approximation are considered. A natural method of constructing such an exponential asymptotics relied on the Borel plane singularity structures provided by the topological expansion is developed. The method is used to form the semiclassical series including exponential contributions for the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure

Measurement and comparison of individual external doses of high-school students living in Japan, France, Poland and Belarus -- the "D-shuttle" project --

Twelve high schools in Japan (of which six are in Fukushima Prefecture), four in France, eight in Poland and two in Belarus cooperated in the measurement and comparison of individual external doses in 2014. In total 216 high-school students and teachers participated in the study. Each participant wore an electronic personal dosimeter "D-shuttle" for two weeks, and kept a journal of his/her whereabouts and activities. The distributions of annual external doses estimated for each region overlap with each other, demonstrating that the personal external individual doses in locations where residence is currently allowed in Fukushima Prefecture and in Belarus are well within the range of estimated annual doses due to the background radiation level of other regions/countries

FROM DYNAMICAL SYSTEMS TO RENORMALIZATION

Abstract. We study in this paper logarithmic derivatives associated to derivations on graded complete Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp–log correspondence between a Lie algebra and its Lie group. Such correspondences occur naturally in the study of dynamical systems when dealing with the linearization of vector fields and the non–linearizability of a resonant vector fields corresponds to the non–invertibility of a logarithmic derivative and to the existence of normal forms. These concepts, stemming from the theory of dynamical systems, can be rephrased in the abstract setting of Lie algebra and the same difficulties as in perturbative quantum field theory (pQFT) arise here. Surprisingly, one can adopt the same ideas as in pQFT with fruitful results such as new constructions of normal forms with the help of the Birkhoff decomposition. The analogy goes even further (locality of counter terms, choice of a renormalization scheme) and shall lead to more interactions between dynamical systems and quantum field theory. hal-00794157, version 1- 25 Feb 2013 1. Introduction. Since the work of A. Connes and D.K Kreimer (see [3], [4]) in perturbative quantum field theory (pQFT), it has been possible to havea purely algebraicinterpretation of some renormalizationschemes

INFLUENCE DE LA DATE DE LA PRÉCOUPE DE LA LUZERNE (MEDICAGO SATIYA L.) SUR SA POLLINISATION

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Effet d'entraînements bi-modaux à la connaissance des lettres : approche développementale

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