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arXiv · 2603.05954

Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time

Hemant Bansal·Alok Maharana·Lingaraj Sahu·Kalyan B. Sinha
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Abstract

The Friedrichs model~\cite{Friedrichs} is revisited to obtain precise results about the asymptotic behaviour (the so-called Breit-Wigner formula~\cite{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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Hemant Bansal, Alok Maharana, Lingaraj Sahu, Kalyan B. Sinha. 2026-03-06. Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time. https://doi.org/10.1016/j.jmaa.2025.130373

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