Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time
Abstract
The Friedrichs model~Friedrichs is revisited to obtain precise results about the asymptotic behaviour (the so-called Breit-Wigner formula~Breit) of a resonance near an embedded eigenvalue and the ``spectral concentration" results as a corollary. Some of the abstract results involved can also be used to address similar questions about a rank-one perturbation of the Laplacian. Exact asymptotic properties are also obtained for the sojourn time, the scattering amplitude and time delay.
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