2011/03/08 by F. Mintert, Florian Mintert, M. Lapert +6
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Medicine · Physics and Astronomy · #Advanced MRI Techniques and Applications #Advanced NMR Techniques and Applications #Derivative (finance) #Electron Spin Resonance Studies #Generalization #Lyapunov function #Magnetic field #Mathematical analysis #Mathematics #Nonlinear system #Physics #Quantum mechanics #Saturation (graph theory) #Spin (aerodynamics) #Thermodynamics #quant-ph
paper · pdf · doi:10.1088/1367-2630/13/7/073001
12 pages, 4 figures, submitted to new journal of physics (2011)
arxiv created 2011/03/08 · openalex publication_date 2011/07/05 · arxiv updated 2015/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show how to apply a generalization of local control design to the problem of the saturation of a spin-1/2 particle by magnetic fields in nuclear magnetic resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with that of the time-optimal solution that has recently been derived using geometric methods.