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

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2015

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https://doi.org/10.1137/1.9781611974072.34
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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, 2015, pp. 244-250. ISBN 978-1-61197-407-2. Available under: doi: 10.1137/1.9781611974072.34

Zusammenfassung

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.

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510 Mathematik

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SIAM Conference on Control and its Applications 2015, 8. Juli 2015 - 10. Juli 2015, Paris, France
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ISO 690CIARAMELLA, Gabriele, 2015. Towards a minimum L2-norm exact control of the Pauli equation. SIAM Conference on Control and its Applications 2015. Paris, France, 8. Juli 2015 - 10. Juli 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, 2015, pp. 244-250. ISBN 978-1-61197-407-2. Available under: doi: 10.1137/1.9781611974072.34
BibTex
@inproceedings{Ciaramella2015-08-07Towar-41231,
  year={2015},
  doi={10.1137/1.9781611974072.34},
  title={Towards a minimum L<sup>2</sup>-norm exact control of the Pauli equation},
  isbn={978-1-61197-407-2},
  publisher={SIAM},
  address={Philadelphia, PA},
  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}
}
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