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RESEARCH PRODUCT
Application of the Pontryagin maximum principle to the time-optimal control in a chain of three spins with unequal couplings
Léo Van DammeRobert ZeierSteffen J. GlaserDominique Sugnysubject
PhysicsAngular momentumSpinsQuantum mechanicsMathematical analysisElliptic functionElliptic integralRigid bodyOptimal controlAtomic and Molecular Physics and OpticsHamiltonian (control theory)Hamiltonian systemdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-07-10 | Physical Review A |