On the role of reachability and observability in NMR experimentation
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered.
- R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, 1987).
- S.J. Glaser, T. Schulte-Herbrüggeen, M. Sieveking, O. Schedletzky, N. Nielsen, O. Sorensen and C. Griesinger, Unitary control in quantum ensembles: maximizing signal intensity in coherent spectroscopy, Science 280 (1998) 421–424. CrossRef
- K. Grasse, Reachability of interior states by piecewise constant controls, Forum Math. 7 (1995) 607–628. CrossRef
- K. Grasse and H.J. Sussmann, Global controllability by nice controls, in: Nonlinear Controllability and Optimal Control, ed. H. Sussmann (Dekker, 1990) pp. 33–79.
- A. Isidori, Nonlinear Control Systems, 3rd ed. (Springer, 1995).
- V. Jurdjevic, Geometric Control Theory (Cambridge University Press, 1997).
- V. Jurdjevic and H.J. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972) 313–329. CrossRef
- S. Lloyd, Phys. Rev. Lett. 75 (1995) 346. CrossRef
- R.J. Ober and E.S. Ward, A system theoretic formulation of NMR experiments, J. Math. Chem. 20 (1996) 47–65. CrossRef
- R.J. Ober and E.S. Ward, On the class of attainable NMR experiments, J. Math. Chem. 22 (1997) 1–10. CrossRef
- V. Ramakrishna and H. Rabitz, Phys. Rev. A 54(2) (1995) 1715. CrossRef
- V. Ramakrishna, M.V. Salapaka, M. Dahleh, H. Rabitz and A. Peirce, Controllability of molecular systems, Phys. Rev. A 51 (1995) 960–966. CrossRef
- T. Untidt, T. Schulte-Herbrüggen, B. Luy, S. Glaser, C. Griesinger, O. Sorensen and N.C. Nielsen, Design of NMR pulse experiments with optimum sensitivity: coherence-order-selective transfer in I 2 S and I 3 S spin systems, Molec. Phys. 95(5) (1998) 787–796. CrossRef
- On the role of reachability and observability in NMR experimentation
Journal of Mathematical Chemistry
Volume 26, Issue 1-3 , pp 15-26
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Author Affiliations
- 1. Center for Engineering Mathematics, University of Texas at Dallas, Richardson, TX, 75083, USA
- 2. Cancer Immunobiology Center and Center for Immunology, University of Texas Southwestern Medical Center, 5323 Harry Hines Boulevard, Dallas, TX, 75235‐8576, USA