Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time
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| Format: | Preprint |
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2026
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| _version_ | 1866911492618584064 |
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| author | Bansal, Hemant Maharana, Alok Sahu, Lingaraj Sinha, Kalyan B. |
| author_facet | Bansal, Hemant Maharana, Alok Sahu, Lingaraj Sinha, Kalyan B. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_05954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time Bansal, Hemant Maharana, Alok Sahu, Lingaraj Sinha, Kalyan B. Spectral Theory Mathematical Physics 47A10, 47A55, 81Q15 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. |
| title | Shape-Resonance in Spectral density, Scattering Cross-section, Time delay and Bound on Sojourn time |
| topic | Spectral Theory Mathematical Physics 47A10, 47A55, 81Q15 |
| url | https://arxiv.org/abs/2603.05954 |