Symmetries of the master equation and long-lived states of nuclear spins.

In terms of the master equation of relaxation, long-lived states in systems of n interacting spin-1/2 nuclei are described as those with eigenvalues much less than the characteristic T(1) rate. It is demonstrated that degeneracies of correlations between interacting dipole-dipole pairs are responsible for their presence. The case n=3 is considered in full detail.

Two-level systems with relaxation.

A method is presented for the coherent control of two-level systems when T2 relaxation is significant. The Bloch equations are rewritten as an equation of motion of the stereographic projection, Gamma, of the spin vector. This allows a Schur-type iteration used for the design of shaped pulses in magnetic resonance and coherent optics to be extended to include the effect of T2.