Holomorphic extension of the de Gennes function

This note is devoted to prove that the de Gennes function has a holomorphic extension on a strip containing the real axis

Magnetic WKB Constructions

This paper is devoted to the semiclassical magnetic Laplacian. Until now WKB expansions for the eigenfunctions were only established in presence of a non-zero electric potential. Here we tackle the pure magnetic case. Thanks to Feynman-Hellmann type formulas and coherent states decomposition, we develop here a magnetic Born-Oppenheimer theory. Exploiting the multiple scales of the problem, we are led to solve an effective eikonal equation in pure magnetic cases and to obtain WKB expansions. We also investigate explicit examples for which we can improve our general theorem: global WKB expansions, quasi-optimal estimates of Agmon and upper bound of the tunelling effect (in symmetric cases). We also apply our strategy to get more accurate descriptions of the eigenvalues and eigenfunctions in a wide range of situations analyzed in the last two decades

Winding vector: how to annihilate two Dirac points with the same charge

The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite ($+-$ scenario) or identical ($++$ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the {\it same} winding number emerge under appropriate distortion (interaction, etc), following the $++$ scenario. Under further distortion, these Dirac points merge following the $+-$ scenario, that is corresponding to {\it opposite} winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.Comment: 5 pages, 6 figure

Statistical mechanics approach to the electric polarization and dielectric constant of band insulators

We develop a theory for the analytic computation of the free energy of band insulators in the presence of a uniform and constant electric field. The two key ingredients are a perturbation-like expression of the Wannier-Stark energy spectrum of electrons and a modified statistical mechanics approach involving a local chemical potential in order to deal with the unbounded spectrum and impose the physically relevant electronic filling. At first order in the field, we recover the result of King-Smith, Vanderbilt, and Resta for the electric polarization in terms of a Zak phase—albeit at finite temperature—and, at second order, deduce a general formula for the electric susceptibility, or equivalently for the dielectric constant. Advantages of our method are the validity of the formalism both at zero and finite temperature and the easy computation of higher order derivatives of the free energy. We verify our findings on two different one-dimensional tight-binding models

Competition between Spin Echo and Spin Self-Rephasing in a Trapped Atom Interferometer

We perform Ramsey interferometry on an ultracold 87Rb ensemble confined in an optical dipoletrap. We use a \pi-pulse set at the middle of the interferometer to restore the coherence of the spinensemble by canceling out phase inhomogeneities and creating a spin echo in the contrast. However,for high atomic densities, we observe the opposite behavior: the \pi-pulse accelerates the dephasingof the spin ensemble leading to a faster contrast decay of the interferometer. We understand thisphenomenon as a competition between the spin-echo technique and an exchange-interaction drivenspin self-rephasing mechanism based on the identical spin rotation effect. Our experimental data iswell reproduced by a numerical model

Visual and interactive tool for product development process enhancement: towards intuitive support of co-located project review

Part 2: PLM EcosystemInternational audienceProduct life management refers to every method or tools which participate to the collaboration of actors involved along the product life. The main topic concerns the organization of this cycle by mastering the evolution between its various phases. Collaboration is a main bottleneck since every phase will involve different experts. The main issue in collaboration is to ensure a good understanding of requirements and constraints of collaborators and to manage conflicts between different experts. Negotiations are expected to solve potential conflicts. This is usually done in project review where the experts must converge towards a common solution. In this paper we investigate the efficiency of a tool formalizing and structuring the project review activity. This tool takes advantage of emerging technologies, here a multi-touch table. We illustrate the discussion with a use case concerning the development of personal computer housing

Semiclassical tunneling and magnetic flux effects on the circle

International audienceThis paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electric wells are connected by two geodesics for the Agmon distance, we highlight an oscillating factor (related to the circulation of the magnetic field) in the splitting estimate of the first two eigenvalues