Bibtex de la publication

@InProceedings{ CaCoGe2011.1,
author = {Caillau, Jean-Baptiste and Cots, Olivier and Gergaud, Joseph},
title = "{Energy minimization in two-level dissipative quantum control : The integrable case (regular paper)}",
booktitle = "{AIMS conference on Dynamical Systems, Differential Equations and Applications, Dresden, 25/05/2010-28/05/2010}",
year = {2011},
publisher = {American Institute of Mathematical Sciences (AIMS)},
address = {},
pages = {198--208},
language = {anglais},
URL = {},
abstract = {The aim of this contribution is to refine some of the computations of [6]. The Lindblad equation modelling a two-level dissipative quantum sys- tem is investigated. The control can be interpretated as the action of a laser to rotate a molecule in gas phase, or as the effect of a magnetic field on a spin 1/2 particle. For the energy cost, normal extremals of the maximum principle are solution to a three-dimensional Hamiltonian with parameters. The analy- sis is focussed on an integrable submodel which defines outside singularities a pseudo-Riemannian metric in dimension five. Complete quadratures are given for this subcase by means of WeierstraƟ elliptic functions. Preliminary com- putations of cut and conjugate loci are also provided for a two-dimensional restriction using [9].}