Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances

Jean-François Bony; Setsuro Fujiié; Thierry Ramond; Maher Zerzeri

Displaying similar documents to “Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances”

Microlocalization of resonant states and estimates of the residue of the scattering amplitude

Jean-François Bony, Laurent Michel (2003)

Journées équations aux dérivées partielles

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We obtain some microlocal estimates of the resonant states associated to a resonance $z_{0}$ of an $h$ -differential operator. More precisely, we show that the normalized resonant states are $𝒪 (\sqrt{| Im z_{0} | / h}$ $+ h^{\infty})$ outside the set of trapped trajectories and are $𝒪 (h^{\infty})$ in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove...

Propagation through trapped sets and semiclassical resolvent estimates

Kiril Datchev, András Vasy (2012)

Annales de l’institut Fourier

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Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.

Scattering amplitude for the Schrödinger equation with strong magnetic field

Laurent Michel (2005)

Journées Équations aux dérivées partielles

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In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.

Asymptotic expansion in time of the Schrödinger group on conical manifolds

Xue Ping Wang (2006)

Annales de l’institut Fourier

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For Schrödinger operator $P$ on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of $P$ near zero. Long-time expansion of the Schrödinger group $U (t) = e^{- i t P}$ is obtained under a non-trapping condition at high energies.

Global existence for coupled Klein-Gordon equations with different speeds

Pierre Germain (2011)

Annales de l’institut Fourier

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Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.