تقرير
Global approximate controllability of quantum systems by form perturbations and applications
| العنوان: | Global approximate controllability of quantum systems by form perturbations and applications |
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| المؤلفون: | Balmaseda, Aitor, Lonigro, Davide, Pérez-Pardo, Juan Manuel |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Mathematical Physics, Mathematics - Functional Analysis, 81Q93, 35Q41, 35J10, 46N50, 47A55, 81Q15 |
| الوصف: | 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 Schr\"odinger 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. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.02955 |
| رقم الأكسشن: | edsarx.2402.02955 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |