Egorov's theorem in the Weyl--Hörmander calculus
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929616950657024 |
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| author | Prouff, Antoine |
| author_facet | Prouff, Antoine |
| contents | We prove a general version of Egorov's theorem for evolution propagators in the Euclidean space, in the Weyl--Hörmander framework of metrics on the phase space. Mild assumptions on the Hamiltonian allow for a wide range of applications that we describe in the paper, including Schrödinger, wave and transport evolutions. We also quantify an Ehrenfest time and describe the full symbol of the conjugated operator. Our main result is a consequence of a stronger theorem on the propagation of quantum partitions of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04320 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Egorov's theorem in the Weyl--Hörmander calculus Prouff, Antoine Analysis of PDEs 35S30, 81Q20, 81S30, 35S05, 47D06 We prove a general version of Egorov's theorem for evolution propagators in the Euclidean space, in the Weyl--Hörmander framework of metrics on the phase space. Mild assumptions on the Hamiltonian allow for a wide range of applications that we describe in the paper, including Schrödinger, wave and transport evolutions. We also quantify an Ehrenfest time and describe the full symbol of the conjugated operator. Our main result is a consequence of a stronger theorem on the propagation of quantum partitions of unity. |
| title | Egorov's theorem in the Weyl--Hörmander calculus |
| topic | Analysis of PDEs 35S30, 81Q20, 81S30, 35S05, 47D06 |
| url | https://arxiv.org/abs/2412.04320 |