Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time
Spectral Theory
2026-03-09 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2603.05954,
title = {Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time},
author = {Hemant Bansal and Alok Maharana and Lingaraj Sahu and Kalyan B. Sinha},
journal= {arXiv preprint arXiv:2603.05954},
year = {2026}
}
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22 pages