On the role of reachability and observability in NMR experimentation

  • Raimund J. Ober
  • Viswanath Ramakrishna
  • E. Sally Ward
Article

Abstract

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.

References

  1. [1]
    R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, 1987).Google Scholar
  2. [2]
    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.CrossRefGoogle Scholar
  3. [3]
    K. Grasse, Reachability of interior states by piecewise constant controls, Forum Math. 7 (1995) 607–628.CrossRefGoogle Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    A. Isidori, Nonlinear Control Systems, 3rd ed. (Springer, 1995).Google Scholar
  6. [6]
    V. Jurdjevic, Geometric Control Theory (Cambridge University Press, 1997).Google Scholar
  7. [7]
    V. Jurdjevic and H.J. Sussmann, Control systems on Lie groups, J. Differential Equations 12 (1972) 313–329.CrossRefGoogle Scholar
  8. [8]
    S. Lloyd, Phys. Rev. Lett. 75 (1995) 346.CrossRefGoogle Scholar
  9. [9]
    R.J. Ober and E.S. Ward, A system theoretic formulation of NMR experiments, J. Math. Chem. 20 (1996) 47–65.CrossRefGoogle Scholar
  10. [10]
    R.J. Ober and E.S. Ward, On the class of attainable NMR experiments, J. Math. Chem. 22 (1997) 1–10.CrossRefGoogle Scholar
  11. [11]
    V. Ramakrishna and H. Rabitz, Phys. Rev. A 54(2) (1995) 1715.CrossRefGoogle Scholar
  12. [12]
    V. Ramakrishna, M.V. Salapaka, M. Dahleh, H. Rabitz and A. Peirce, Controllability of molecular systems, Phys. Rev. A 51 (1995) 960–966.CrossRefGoogle Scholar
  13. [13]
    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.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Raimund J. Ober
    • 1
    • 2
  • Viswanath Ramakrishna
    • 1
  • E. Sally Ward
    • 2
  1. 1.Center for Engineering MathematicsUniversity of Texas at DallasRichardsonUSA
  2. 2.Cancer Immunobiology Center and Center for ImmunologyUniversity of Texas Southwestern Medical CenterDallasUSA

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