Symmetry and isotropie coherence transfer II. Multi spin calculations using a young tableaux formulation

A general treatment of spin dynamics during coherence transfer is presented as an example of a many-body problem under strong coupling. In a previous paper, coherence transfer by isotropic mixing (IM) between two coupled spins was examined. However, the greatest experimental interest in the technique of IM centers on the transfer of coherence between spins that are not directly coupled. The dynamics of coherence transfer in multiple spin systems are cast in a superoperator formulation, in which diagonalization of the mixing Liouvillian matrix allows derivation of the coherence transfer frequencies from the eigenvalues. Development of a particular basis of the spin density operator space facilitates diagonalization of the strong coupling Liouvillian. This basis is completely reduced with respect to rotation, permutation, and particle number. Treatment of the many-body aspect is based on an approach using the Young tableaux. The exact calculation of the dynamics of coherence transfer in a three spin system is accomplished using the tableaux method, and closed form solutions are compared with results obtained using numerical methods. The degree to which practical coherence transfer pulse sequences deviate from ideal isotropic mixing, and the effect that these deviations have on symmetryinduced selection rules is calculated numerically.