Width of shape resonances for non globally analytic potentials

DOI10.2969/jmsj/06310001zbMath1210.81037arXiv0811.0734OpenAlexW2085611962MaRDI QIDQ632978

Amina Lahmar-Benbernou, Setsuro Fujiié, André Martinez

Publication date: 28 March 2011

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.0734

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Asymptotic expansions of solutions to PDEs (35C20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Resonance in context of PDEs (35B34)

Related Items (18)

Adiabatic Evolution and Shape Resonances ⋮ Molecular predissociation resonances near an energy-level crossing. I: Elliptic interaction ⋮ Propagation of singularities and resonances ⋮ Semiclassical estimates of the cut-off resolvent for trapping perturbations ⋮ An example of resonance instability ⋮ Semiclassical asymptotic distribution of resonances created by homoclinic and heteroclinic trajectories ⋮ Exponential lower resolvent bounds far away from trapped sets ⋮ Optimal lower bound of the resonance widths for a Helmholtz tube-shaped resonator ⋮ Resonance free regions in magnetic scattering by two solenoidal fields at large separation ⋮ Fractional exponential decay in the forbidden region for Toeplitz operators ⋮ Aharonov-Bohm effect in resonances of magnetic Schrödinger operators in two dimensions ⋮ Resonances in scattering by two magnetic fields at large separation and a complex scaling method ⋮ Barrier-top resonances for non globally analytic potentials ⋮ Mathematical study of scattering resonances ⋮ Widths of highly excited shape resonances ⋮ Widths of highly excited resonances in multidimensional molecular predissociation ⋮ Applications of resonance theory without analyticity assumption ⋮ Optimal lower bound of the resonance widths for the Helmholtz resonator

Cites Work

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• Résonances en limite semi-classique
• Estimations de l'effet tunnel pour le double puits. II : états hautement excités
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