Application of the Pontryagin maximum principle to the time-optimal control in a chain of three spins with unequal couplings

Léo Van Damme, Robert Zeier, Steffen J. Glaser, Dominique Sugny

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Abstract

We solve a time-optimal control problem in a linear chain of three coupled spins 1/2 with unequal couplings. We apply the Pontryagin maximum principle and show that the associated Hamiltonian system is the one of a three-dimensional rigid body. We express the optimal control fields in terms of the components of the classical angular momentum of the rigid body. The optimal trajectories and the minimum control time are given in terms of elliptic functions and elliptic integrals.

Original languageEnglish
Article number013409
JournalPhysical Review A
Volume90
Issue number1
DOIs
StatePublished - 10 Jul 2014

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