Global approximate controllability of quantum systems by form perturbations and applications

Fuente: arXiv
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Main Authors: Balmaseda, Aitor, Lonigro, Davide, Pérez-Pardo, Juan Manuel
Format: Preprint
Published: 2024
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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
id 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