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arXiv · 0908.3444

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

Jean-Francois Bony·Setsuro Fujiie·Thierry Ramond·Maher Zerzeri
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Abstract

We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrodinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of h, and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we give an expansion for large times of the Schrodinger group in terms of these resonances.

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Jean-Francois Bony, Setsuro Fujiie, Thierry Ramond, Maher Zerzeri. 2009-08-24. Spectral projection, residue of the scattering amplitude, and Schrodinger group expansion for barrier-top resonances. https://arxiv.org/abs/0908.3444

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