On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929415296909312 |
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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 the stability of the Schrödinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schrödinger equation by the difference of their Hamiltonians. The stability theorem obtained in this article provides a sharper bound than those previously obtained in the literature. This makes it a potentially useful tool for time-dependent problems in Quantum Physics, in particular for Quantum Control. We apply this result to prove two theorems about global approximate controllability of infinite-dimensional quantum systems. These results improve and generalise existing results on infinite-dimensional quantum control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_10203 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control Balmaseda, Aitor Lonigro, Davide Pérez-Pardo, Juan Manuel Mathematical Physics Functional Analysis Optimization and Control 35Q41, 35J10, 37K45, 81Q93 We study the stability of the Schrödinger equation generated by time-dependent Hamiltonians with constant form domain. That is, we bound the difference between solutions of the Schrödinger equation by the difference of their Hamiltonians. The stability theorem obtained in this article provides a sharper bound than those previously obtained in the literature. This makes it a potentially useful tool for time-dependent problems in Quantum Physics, in particular for Quantum Control. We apply this result to prove two theorems about global approximate controllability of infinite-dimensional quantum systems. These results improve and generalise existing results on infinite-dimensional quantum control. |
| title | On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control |
| topic | Mathematical Physics Functional Analysis Optimization and Control 35Q41, 35J10, 37K45, 81Q93 |
| url | https://arxiv.org/abs/2306.10203 |