Determining metrics from the scattering map of the time-dependent Schrödinger equation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915948626182144 |
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| author | Jia, Qiuye |
| author_facet | Jia, Qiuye |
| contents | For a time dependent Schrödinger equation, the scattering map is the map sending the asymptotic profile of solution as $t\to-\infty$ to its asymptotic profile as $t\to+\infty$. In this paper we show that, for certain class of metrics, the scattering maps associated to two Schrödinger operators with two time dependent metrics only differ by a compact operator if and only if these two metrics are related by a pull-back of a diffeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20160 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Determining metrics from the scattering map of the time-dependent Schrödinger equation Jia, Qiuye Analysis of PDEs Mathematical Physics Differential Geometry 35R30, 35Q41, 35S30, 81U40, 35S05 For a time dependent Schrödinger equation, the scattering map is the map sending the asymptotic profile of solution as $t\to-\infty$ to its asymptotic profile as $t\to+\infty$. In this paper we show that, for certain class of metrics, the scattering maps associated to two Schrödinger operators with two time dependent metrics only differ by a compact operator if and only if these two metrics are related by a pull-back of a diffeomorphism. |
| title | Determining metrics from the scattering map of the time-dependent Schrödinger equation |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry 35R30, 35Q41, 35S30, 81U40, 35S05 |
| url | https://arxiv.org/abs/2604.20160 |