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Convergence of the time-discretized monotonic schemes

Published online by Cambridge University Press:  26 April 2007

Julien Salomon
Julien Salomon*
Affiliation:
Université Pierre et Marie Curie, Paris 6, Laboratoire Jacques-Louis Lions, 175 rue du Chevaleret 75013 Paris, France. Université Paris-Dauphine, Paris 9, CEREMADE, Place du Maréchal Lattre de Tassigny, 75775 Paris Cedex 16, France. Julien.Salomon@dauphine.fr
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Abstract

Many numerical simulations in (bilinear) quantum control use the monotonically convergent Krotov algorithms (introduced byTannor et al. [Time Dependent Quantum Molecular Dynamics (1992) 347–360]), Zhu and Rabitz [J. Chem. Phys. (1998) 385–391] or theirunified form described in Maday and Turinici [J. Chem. Phys. (2003) 8191–8196]. InMaday et al. [Num. Math. (2006) 323–338], a time discretization which preserves theproperty of monotonicity has been presented. This paper introduces aproof of the convergence of these schemes and some results regarding theirrate of convergence.

Keywords

Quantum controlmonotonic schemesoptimal controlŁojasiewicz inequality.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 1 , January 2007 , pp. 77 - 93
Copyright
© EDP Sciences, SMAI, 2007

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