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A Globalized Newton Method for the Optimal Control of Fermionic Systems

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Control and Optimization with PDE Constraints

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 164))

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Abstract

A computational framework for determining optimal control fields for inducing energy state transitions in systems of several fermions in an infinite potential quantum well is presented. The full multiparticle system is numerically approximated using linear combinations of Slater determinants constructed from nodal trial functions, which leads to diagonalized matrix approximations of variable coefficient terms. First and second order optimality conditions are given for the control and a robust line search is described for computing a local minimizer.

This work was supported by the Austrian Science Fund (FWF) under grant SFB F32 (SFB “Mathematical Optimization and Applications in Biomedical Sciences”).

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Author notes

  1. Gregory von Winckel

    Present address: Center for High Technology Materials, University of New Mexico, 1313 Goddard Street SE, Albuquerque, NM, 87106, USA

Authors and Affiliations

  1. Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, 36 Heinrichstraße, A-8010, Graz, Austria

    Gregory von Winckel

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  1. Gregory von Winckel
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Correspondence to Gregory von Winckel .

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Editors and Affiliations

  1. , Institute for Mathematics and Scientific, University of Graz, Heinrichstr. 36, Graz, 8010, Austria

    Kristian Bredies

  2. , Institute for Mathematics and Scientific, University of Graz, Heinrichstr. 36, Graz, 8010, Austria

    Christian Clason

  3. , Institute for Mathematics and Scientific, University of Graz, Heinrichstr. 36, Graz, 8010, Austria

    Karl Kunisch  & Gregory von Winckel  & 

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von Winckel, G. (2013). A Globalized Newton Method for the Optimal Control of Fermionic Systems. In: Bredies, K., Clason, C., Kunisch, K., von Winckel, G. (eds) Control and Optimization with PDE Constraints. International Series of Numerical Mathematics, vol 164. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0631-2_10

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