Global approximate controllability of quantum systems by form perturbations and applications
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915221777416192 |
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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 provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results on controllability of quantum bilinear control systems and obtain a priori $L^1$-bounds of the controls for generic initial and target states. We apply a stability result for the non-autonomous Schrödinger equation to extend the results to systems defined by form perturbations, including singular perturbations. As an application of our results, we prove approximate controllability of a quantum particle in a one-dimensional box with a point-interaction with tuneable strength at the centre of the box. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_02955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global approximate controllability of quantum systems by form perturbations and applications Balmaseda, Aitor Lonigro, Davide Pérez-Pardo, Juan Manuel Optimization and Control Mathematical Physics Functional Analysis 81Q93, 35Q41, 35J10, 46N50, 47A55, 81Q15 We provide sufficient conditions for the approximate controllability of infinite-dimensional quantum control systems corresponding to form perturbations of the drift Hamiltonian modulated by a control function. We rely on previous results on controllability of quantum bilinear control systems and obtain a priori $L^1$-bounds of the controls for generic initial and target states. We apply a stability result for the non-autonomous Schrödinger equation to extend the results to systems defined by form perturbations, including singular perturbations. As an application of our results, we prove approximate controllability of a quantum particle in a one-dimensional box with a point-interaction with tuneable strength at the centre of the box. |
| title | Global approximate controllability of quantum systems by form perturbations and applications |
| topic | Optimization and Control Mathematical Physics Functional Analysis 81Q93, 35Q41, 35J10, 46N50, 47A55, 81Q15 |
| url | https://arxiv.org/abs/2402.02955 |