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2011, Volume 2011: 198-208. Doi: 10.3934/proc.2011.2011.198 open access
This issue Previous Article Existence for the linearization of a steady state fluid/nonlinear elasticity interaction Next Article Non ordered lower and upper solutions to fourth order problems with functional boundary conditions

Energy minimization in two-level dissipative quantum control: Th e integrable case

  • 1.

    Math. Institute, Bourgogne Univ. & CRNS, 9 avenue Savary, F-21078 Dijon

Received:  July 31, 2010
Revised:  February 28, 2011
Published:  August 2017
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    Abstract
  • The aim of this contribution is to re ne some of the computations of [6]. The Lindblad equation modelling a two-level dissipative quantum system is investigated. The control can be interpretated as the action of a laser to rotate a molecule in gas phase, or as the e ect of a magnetic eld 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 analysis is focussed on an integrable submodel which de nes outside singularities a pseudo-Riemannian metric in dimension ve. Complete quadratures are given for this subcase by means of Weierstra elliptic functions. Preliminary computations of cut and conjugate loci are also provided for a two-dimensional restriction using [9].
    Mathematics Subject Classification: Primary: 49K15, 81Q05.

    Citation:
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