Stationary completeness: the $N$-body short-range case
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929446119800832 |
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| author | Skibsted, Erik |
| author_facet | Skibsted, Erik |
| contents | For a general class of $N$-body Schrödinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. This holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Dereziński-Enss type. In this paper we improve for short-range models on the known weak continuity properties in that we show that all non-threshold energies are stationary complete, resolving in this case a conjecture from [Sk1]. A consequence is that the above scattering quantities depend strongly continuously on the energy parameter at all non-threshold energies (improving on previously almost everywhere proven properties). Another consequence is that the scattering matrix is unitary at any such energy. As a side result we obtain a new and purely stationary proof of asymptotic completeness for $N$-body short-range systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stationary completeness: the $N$-body short-range case Skibsted, Erik Mathematical Physics Spectral Theory For a general class of $N$-body Schrödinger operators with short-range pair-potentials the wave and scattering matrices as well as the restricted wave operators are all defined at any non-threshold energy. This holds without imposing any a priori decay condition on channel eigenstates and even for models including long-range potentials of Dereziński-Enss type. In this paper we improve for short-range models on the known weak continuity properties in that we show that all non-threshold energies are stationary complete, resolving in this case a conjecture from [Sk1]. A consequence is that the above scattering quantities depend strongly continuously on the energy parameter at all non-threshold energies (improving on previously almost everywhere proven properties). Another consequence is that the scattering matrix is unitary at any such energy. As a side result we obtain a new and purely stationary proof of asymptotic completeness for $N$-body short-range systems. |
| title | Stationary completeness: the $N$-body short-range case |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2306.07080 |