On global approximate controllability of a quantum particle in a box by moving walls
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911788136660992 |
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| author | Balmaseda, Aitor Lonigro, Davide Pérez-Pardo, Juan Manuel |
| author_facet | Balmaseda, Aitor Lonigro, Davide Pérez-Pardo, Juan Manuel |
| contents | We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any target state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schrödinger equation and use a stability theorem for the time-dependent Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13475 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On global approximate controllability of a quantum particle in a box by moving walls Balmaseda, Aitor Lonigro, Davide Pérez-Pardo, Juan Manuel Optimization and Control Mathematical Physics Quantum Physics 81Q93, 35Q41, 35R37, 35J10 We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any target state in the Hilbert space of the free particle with a predetermined final position of the box. To this purpose we consider weak solutions of the Schrödinger equation and use a stability theorem for the time-dependent Schrödinger equation. |
| title | On global approximate controllability of a quantum particle in a box by moving walls |
| topic | Optimization and Control Mathematical Physics Quantum Physics 81Q93, 35Q41, 35R37, 35J10 |
| url | https://arxiv.org/abs/2208.13475 |