6533b858fe1ef96bd12b577e
RESEARCH PRODUCT
The energy minimization problem for two-level dissipative quantum systems
Bernard BonnardDominique SugnyNataliya ShcherbakovaOlivier Cotssubject
Numerical analysisComputationMathematical analysisMaster equationConjugate pointsDissipative systemQuantum systemStatistical and Nonlinear PhysicsEnergy minimizationOptimal controlMathematical PhysicsMathematicsdescription
In this article, we study the energy minimization problem of dissipative two-level quantum systems whose dynamics is governed by the Kossakowski–Lindblad equations. In the first part, we classify the extremal curve solutions of the Pontryagin maximum principle. The optimality properties are analyzed using the concept of conjugate points and the Hamilton–Jacobi–Bellman equation. This analysis completed by numerical simulations based on adapted algorithms allows a computation of the optimal control law whose robustness with respect to the initial conditions and dissipative parameters is also detailed. In the final section, an application in nuclear magnetic resonance is presented.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-09-01 | Journal of Mathematical Physics |