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Towards a minimum L<sup>2</sup>-norm exact control of the Pauli equation

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Towards a minimum L2-norm exact control of the Pauli equation

Type of Publication: Contribution to a conference collection
Publication status: Published
Author: Ciaramella, Gabriele
Year of publication: 2015
Conference: SIAM Conference on Control and its Applications 2015, Jul 8, 2015 - Jul 10, 2015, Paris, France
Published in: 2015 Proceedings of the Conference on Control and its Applications / Bonnet, Catherine; Pasik-Duncan, Bozenna; Ozbay, Hitay; Zhang, Qing-Wen (ed.). - Philadelphia, PA : SIAM, 2015. - pp. 244-250. - ISBN 978-1-61197-407-2
DOI (citable link): https://dx.doi.org/10.1137/1.9781611974072.34
Summary:
A computational framework for the exact-control of the magnetic state and the spin of an electron is presented. The evolution of this quantum system is governed by the Pauli equation, that is a system of Schrödinger equations coupled by the action of magnetic fields. The magnetic fields are used as controls in order to steer the quantum system from an initial state to a desired target state at a given final time. This control framework is based on a minimum norm optimization formulation of exact-controllability quantum problems, that allows the application of efficient Krylov-Newton optimization techniques. In order to provide this framework with an adequate initialization, a continuation procedure is discussed. Results of numerical experiments demonstrate the effectiveness of the proposed framework.
Subject (DDC): 510 Mathematics

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CIARAMELLA, Gabriele, 2015. Towards a minimum L2-norm exact control of the Pauli equation. SIAM Conference on Control and its Applications 2015. Paris, France, Jul 8, 2015 - Jul 10, 2015. In: BONNET, Catherine, ed., Bozenna PASIK-DUNCAN, ed., Hitay OZBAY, ed., Qing-Wen ZHANG, ed.. 2015 Proceedings of the Conference on Control and its Applications. Philadelphia, PA:SIAM, pp. 244-250. ISBN 978-1-61197-407-2. Available under: doi: 10.1137/1.9781611974072.34

@inproceedings{Ciaramella2015-08-07Towar-41231, title={Towards a minimum L2-norm exact control of the Pauli equation}, year={2015}, doi={10.1137/1.9781611974072.34}, isbn={978-1-61197-407-2}, address={Philadelphia, PA}, publisher={SIAM}, booktitle={2015 Proceedings of the Conference on Control and its Applications}, pages={244--250}, editor={Bonnet, Catherine and Pasik-Duncan, Bozenna and Ozbay, Hitay and Zhang, Qing-Wen}, author={Ciaramella, Gabriele} }

2018-02-05T14:30:51Z Ciaramella, Gabriele 2018-02-05T14:30:51Z Towards a minimum L<sup>2</sup>-norm exact control of the Pauli equation eng A computational framework for the exact-control of the magnetic state and the spin of an electron is presented. The evolution of this quantum system is governed by the Pauli equation, that is a system of Schrödinger equations coupled by the action of magnetic fields. The magnetic fields are used as controls in order to steer the quantum system from an initial state to a desired target state at a given final time. This control framework is based on a minimum norm optimization formulation of exact-controllability quantum problems, that allows the application of efficient Krylov-Newton optimization techniques. In order to provide this framework with an adequate initialization, a continuation procedure is discussed. Results of numerical experiments demonstrate the effectiveness of the proposed framework. 2015-08-07 Ciaramella, Gabriele

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