1. Global approximate controllability of quantum systems by form perturbations and applications
- Author
-
Balmaseda, Aitor, Lonigro, Davide, and Pérez-Pardo, Juan Manuel
- Subjects
Mathematics - Optimization and Control ,Mathematical Physics ,Mathematics - Functional Analysis ,81Q93, 35Q41, 35J10, 46N50, 47A55, 81Q15 - Abstract
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
- Published
- 2024