Displaying similar documents to “Asymptotic behavior of regularized scattering phases for long range perturbations”

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 ( | Im z 0 | / h + h ∞ ) outside the set of trapped trajectories and are 𝒪 ( h ∞ ) 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...

Weyl type upper bounds on the number of resonances near the real axis for trapped systems

Plamen Stefanov (2001)

Journées équations aux dérivées partielles

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We study semiclassical resonances in a box Ω ( h ) of height h N , N ≫ 1 . We show that the semiclassical wave front set of the resonant states (including the “generalized eigenfunctions”) is contained in the set 𝒯 of the trapped bicharacteristics. We also show that for a suitable self-adjoint reference operator P # ( h ) with discrete spectrum the number of resonances in Ω ( h ) is bounded by the number of eigenvalues of P # ( h ) in an interval a bit larger than the projection of Ω ( h ) on the real line. As an application,...

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.

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.

Resonances for Schrödinger operators with compactly supported potentials

T. J. Christiansen, P. D. Hislop (2008)

Journées Équations aux dérivées partielles

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We describe the generic behavior of the resonance counting function for a Schrödinger operator with a bounded, compactly-supported real or complex valued potential in d ≥ 1 dimensions. This note contains a sketch of the proof of our main results [, ] that generically the order of growth of the resonance counting function is the maximal value d in the odd dimensional case, and that it is the maximal value d on each nonphysical sheet of the logarithmic Riemann surface in the even dimensional...