Abstract
We consider the nuclear magnetic resonance (NMR) problem of calculating the Carr-Purcell-Meiboom-Gill (CPMG) echo sequence for spins diffusing in a porous medium in a general magnetic field. We present explicit comparisons between the exact value of the echo sequence and the results predicted asymptotically at the boundaries of the space of parameters of the experiment. We also suggest an exponential term correction to the subleading “boundary” term in the short-time asymptotic formula, which is analogous to the exponential used in quantum field theoretic perturbation theory when going from connected to disconnected Feynman graphs. We discuss briefly how the results presented here answer questions that are analogous to basic questions in geometrical quantum field theory.
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References
Major developments in M-theory and string theory have been coming out at such a pace that it is hard to give an up to date reference. One recent review available on the web is: M.J.Duff, State of the unification address, http://xxx.lanl.gov/abs/hep-th70012249. We refer the reader to references cited there.
M.F. Atiyah, New invariants of three and four dimensional manifolds, in The mathematical heritage of Hermann Weyl, Proc. Symp. Pure Math., vol. 48, ed. R. Wells, Providence, RI, 1988. M.F. Atiyah, The Geometry and Physics of Knots, Cambridge U. Press, Cambridge, 1990.
E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys., 121,351,(1989).
E. L. Hahn, Phys. Rev., 80, 580, (1950)
H. Y. Carr and E. M. Purcell, Phys. Rev., 94, 630, (1954)
S. Meiboom and D. Gill Rev. Sci. Instr. 29, 688 (1958).
S. Axelrod and P.N. Sen, Nuclear magnetic resonance spin echoes for restricted diffusion in an inhomogeneous field: Methods for asymptotic regimes, J. Chem. Phys. 114 (2001).
H. C. Torrey, Phys. Rev. 104, 563 (1956)
P. N. Sen, A. André, S. Axelrod, Spin echoes of nuclear magnetization diffusing in a constant magnetic field gradient and in a restricted geometry, J. Chem. Phys., 111, 6548, (1999).
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Axelrod, S. (2001). Geometry, Quantum Field Theory and NMR. In: Khuri, R.R., Liu, J.T., Chen, F., Gan, W. (eds) The Universality of Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0585-3_7
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DOI: https://doi.org/10.1007/978-1-4615-0585-3_7
Publisher Name: Springer, Boston, MA
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