Inverse scattering for $N$-body time-decaying harmonic oscillators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912832773160960 |
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| author | Ishida, Atsuhide |
| author_facet | Ishida, Atsuhide |
| contents | In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a two-body quantum system described by time-decaying harmonic oscillators. In this study, we extend the result of Ishida (2025) to the $N$-body case. We use the approaches developed in Enss and Weder (1995), Weder (1996), and Valencia and Weder (2012) to prove that the high-velocity limit of the scattering operator uniquely determines all the pairwise interaction potentials among the $N$ particles, focusing respectively on each fixed pair of particles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse scattering for $N$-body time-decaying harmonic oscillators Ishida, Atsuhide Mathematical Physics Analysis of PDEs In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a two-body quantum system described by time-decaying harmonic oscillators. In this study, we extend the result of Ishida (2025) to the $N$-body case. We use the approaches developed in Enss and Weder (1995), Weder (1996), and Valencia and Weder (2012) to prove that the high-velocity limit of the scattering operator uniquely determines all the pairwise interaction potentials among the $N$ particles, focusing respectively on each fixed pair of particles. |
| title | Inverse scattering for $N$-body time-decaying harmonic oscillators |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04702 |