Scattering for Schrödinger operators with conical decay
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912222699061248 |
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| author | Black, Adam Malinovitch, Tal |
| author_facet | Black, Adam Malinovitch, Tal |
| contents | We study the scattering properties of Schrödinger operators with potentials that have short-range decay along a collection of rays in $\bbR^d$. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along \emph{all} rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece which may interact with the potential for long times. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10596 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scattering for Schrödinger operators with conical decay Black, Adam Malinovitch, Tal Mathematical Physics Analysis of PDEs Spectral Theory We study the scattering properties of Schrödinger operators with potentials that have short-range decay along a collection of rays in $\bbR^d$. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along \emph{all} rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece which may interact with the potential for long times. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial. |
| title | Scattering for Schrödinger operators with conical decay |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2210.10596 |