Energy Minimization Problem in Two-Level Dissipative Quantum Control: Meridian Case
- 82 Downloads
We analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky–Lindblad equation. According to the Pontryagin maximum principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous analysis from  concerning 2D solutions in the case where the Hamiltonian dynamics are integrable.
Unable to display preview. Download preview PDF.
- 3.B. Bonnard and M. Chyba, “Singular trajectories and their role in control theory,” in: Math. Appl., 40, Springer-Verlag, Berlin (2003).Google Scholar
- 4.B. Bonnard and J.-B. Caillau, Singular Metrics on the Two-Sphere in Space Mechanics, HAL (2008).Google Scholar
- 6.B. Bonnard, J.-B. Caillau, and O. Cots, “Energy minimization in two-level dissipative quantum control: the integrable case,” in: Proc. 8th AIMS Conf. on Dynamical Systems, Differential Equations and Applications, Dresden (2011), pp. 198–208.Google Scholar
- 7.U. Boscain and P. Mason, “Time minimal trajectories for a spin 1/2 particle in a magnetic field,” J. Math. Phys., 47, No. 6 (2006).Google Scholar
- 8.J. B. Caillau, O. Cots, and J. Gergaud, Hampath, apo.enseeiht.fr/hampath.Google Scholar
- 10.H. T. Davies, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York (1962).Google Scholar
- 12.V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press (1960).Google Scholar