On the guided states of 3D biperiodic Schrödinger operators

International audienceWe consider the Laplacian operator H_0 perturbed by a non-positive potential $V$, which is periodic in two directions, and decays in the remaining one. We are interested in the characterization and decay properties of the guided states, defined as the eigenfunctions of the reduced operators in the Bloch-Floquet-Gelfand transform of H_0+V in the periodic variables. If V is sufficiently small and decreases fast enough in the infinite direction, we prove that, generically, these guided states are characterized by quasi-momenta belonging to some one-dimensional compact real analytic submanifold of the Brillouin zone. Moreover they decay faster than any polynomial function in the infinite direction

Sub-linear capacity scaling for multi-path channel models

International audienceThe theoretic capacity of a communication system constituted of several transmitting/receiving elements is determined by the singular values of its transfer matrix. Results based on an independent identically distributed channel model, representing an idealized rich propagation environment, state that the capacity is directly proportional to the number of antennas. Nevertheless there is growing experimental evidence that the capacity gain can at best scale at a sub-linear rate with the system size. In this paper, we show under appropriate assumptions on the transfer matrix of the system, that the theoretic information-capacity of multi-antenna systems is upper bounded by a sub-linear function of the number of transmitting/receiving links

Analysing the scattering of electromagnetic ultra wide band pulses from large scale objects by the use of wavelets

The aim of this paper is the study of the signal received by an antenna (RX) when a transmit antenna (TX) sends a short pulse in a large scale space, for instance, in an urban environment. Integral equations are established which link the densities of charges and currents inside the environment objects with the incident field created by the TX antenna. From this equations we define an integral operator K. The densities can be obtained inverting 1 − K. The introduction of Daubechies wavelets allows us to obtain sparse matrices for KK * which is computationally convenient to get (1 − K) −1

An expression for attenuation in deformed optical waveguides

In this paper we study the effect of random microdeformations on the radiation propagation in optical waveguides. We use the localization ideas coming from solid state physics. In particular we deduce a formula linking the attenuation in a single mode fiber to the autocorrelation function of random bends.Nous étudions dans cet article les effets de micro-déformations aléatoires sur la propagation des ondes électromagnétiques dans les fibres optiques. Utilisant les techniques mises en œuvre pour l'étude de la localisation en physique du solide, nous donnons, en particulier pour une fibre mono-mode, l'expression de l'atténuation en fonction de la distribution des micro-courbures aléatoires

Influence of Environment Richness on the Increase of MIMO Capacity With Number of Antennas

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On the Dynamics of Crystal Electrons, high Momentum Regime

16 pagesWe study the quantum dynamics generated by $H^{SW}=-{d^2\\over dx^2}+V-x$ with $V$ a real periodic function of weak regularity. We prove that the continuous spectrum of $H^{SW}$ is never empty, and furthermore that for $V$ small enough there are no bound states

Contributions to the mathematical theory of transport phenomena

AIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF