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Convergence of the time-discretized monotonic schemes

Published online by Cambridge University Press:  26 April 2007

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. [email protected]
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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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2007

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