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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2402.19219 |
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| _version_ | 1866909123396763648 |
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| author | Assal, Marouane fujiie, Setsuro Higuchi, Kenta |
| author_facet | Assal, Marouane fujiie, Setsuro Higuchi, Kenta |
| contents | We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schrödinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point with contact order $n$, the corresponding two classical trajectories at the crossing level intersect at one point in the phase space with contact order $2n$. We compute the transfer matrix at this point between the incoming and outgoing microlocal solutions and apply it to the semiclassical distribution of resonances at the energy crossing level. It is described in terms of a generalized Airy function. This result generalizes \cite{FMW1} to the tangential crossing and \cite{AFH1} to the crossing at a turning point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19219 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transition of the semiclassical resonance widths across a tangential crossing energy-level Assal, Marouane fujiie, Setsuro Higuchi, Kenta Mathematical Physics Spectral Theory We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schrödinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point with contact order $n$, the corresponding two classical trajectories at the crossing level intersect at one point in the phase space with contact order $2n$. We compute the transfer matrix at this point between the incoming and outgoing microlocal solutions and apply it to the semiclassical distribution of resonances at the energy crossing level. It is described in terms of a generalized Airy function. This result generalizes \cite{FMW1} to the tangential crossing and \cite{AFH1} to the crossing at a turning point. |
| title | Transition of the semiclassical resonance widths across a tangential crossing energy-level |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2402.19219 |