Quantum Flux and Quantum Ergodicity for Cross Sections
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910397156556800 |
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| author | Christianson, Hans Toth, John |
| author_facet | Christianson, Hans Toth, John |
| contents | For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $Σ$ of a non-degenerate energy surface. We prove restrictions of eigenfunctions to $Σ$, realized using the quantum flux norm, are quantum ergodic. We compare this result to known results from \cite{CTZ} in the case of Euclidean domains and hyperfurfaces. As a further application, we consider complexified analytic eigenfunctions and prove a second microlocal analogue of \cite{CTZ} in that context. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_02296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Flux and Quantum Ergodicity for Cross Sections Christianson, Hans Toth, John Analysis of PDEs Mathematical Physics 35B40, 35P99, 58J51 For sequences of quantum ergodic eigenfunctions, we define the quantum flux norm associated to a codimension $1$ submanifold $Σ$ of a non-degenerate energy surface. We prove restrictions of eigenfunctions to $Σ$, realized using the quantum flux norm, are quantum ergodic. We compare this result to known results from \cite{CTZ} in the case of Euclidean domains and hyperfurfaces. As a further application, we consider complexified analytic eigenfunctions and prove a second microlocal analogue of \cite{CTZ} in that context. |
| title | Quantum Flux and Quantum Ergodicity for Cross Sections |
| topic | Analysis of PDEs Mathematical Physics 35B40, 35P99, 58J51 |
| url | https://arxiv.org/abs/2404.02296 |