Browsing by Author "Briet, Philippe"

Now showing 1 - 3 of 3
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    Eigenvalue Asymptotics in a Twisted Waveguide
    (TAYLOR & FRANCIS INC, 2009) Briet, Philippe; Kovarik, Hynek; Raikov, Georgi; Soccorsi, Eric
    We consider a twisted quantum wave guide i.e., a domain of the form :=r x where 2 is a bounded domain, and r=r(x3) is a rotation by the angle (x3) depending on the longitudinal variable x3. We are interested in the spectral analysis of the Dirichlet Laplacian H acting in L2(). We suppose that the derivative [image omitted] of the rotation angle can be written as [image omitted](x3)=-epsilon(x3) with a positive constant and epsilon(x3) L|x3|-, |x3|. We show that if L0 and (0,2), or if LL00 and =2, then there is an infinite sequence of discrete eigenvalues lying below the infimum of the essential spectrum of H, and obtain the main asymptotic term of this sequence.
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    Exponential decay and resonances in a driven system
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2012) Briet, Philippe; Fernandez, Claudio
    We study the resonance phenomena for time periodic perturbations of a Hamiltonian H on the Hilbert space L-2 (R-d). Here, resonances are characterized in terms of time behavior of the survival probability. Our approach uses the Floquet-Howland formalism combined with the results of L. Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent perturbations. (C) 2012 Elsevier Inc. All rights reserved.
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    Spectral properties of a magnetic quantum Hamiltonian on a strip
    (IOS PRESS, 2008) Briet, Philippe; Raikov, Georgi; Soccorsi, Eric
    We consider a 2D Schrodinger operator H(0) with constant magnetic field, on a strip of finite width. The spectrum of H(0) is absolutely continuous, and contains a discrete set of thresholds. We perturb H(0) by an electric potential V which decays in a suitable sense at infinity, and study the spectral properties of the perturbed operator H = H(0) + V. First, we establish a Mourre estimate, and as a corollary prove that the singular continuous spectrum of H is empty, and any compact subset of the complement of the threshold set may contain at most a finite set of eigenvalues of H, each of them having a finite multiplicity. Next, we introduce the Krein spectral shift function (SSF) for the operator pair (H, H(0)). We show that this SSF is bounded on any compact subset of the complement of the threshold set, and is continuous away from the threshold set and the eigenvalues of H. The main results of the article concern the asymptotic behaviour of the SSF at the thresholds, which is described in terms of the SSF for a pair of effective Hamiltonians.