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Communication Dans Un Congrès Année : 2012

Which notion of energy for bilinear quantum systems?

Résumé

In this note we investigate what is the best L^p-norm in order to describe the relation between the evolution of the state of a bilinear quantum system with the L^p-norm of the external field. Although L^2 has a structure more easy to handle, the L^1 norm is more suitable for this purpose. Indeed for every p>1, it is possible to steer, with arbitrary precision, a generic bilinear quantum system from any eigenstate of the free Hamiltonian to any other with a control of arbitrary small L^p norm. Explicit optimal costs for the L^1 norm are computed on an example.
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Dates et versions

hal-00784890 , version 1 (04-02-2013)

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Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Which notion of energy for bilinear quantum systems?. LHMNLC - 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control - 2012, Aug 2012, Bertinoro, Italy. pp.226-230. ⟨hal-00784890⟩
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