Theory of scalar relaxation of the second kind. II

Publisher Website
Google Scholar
Abstract
A previously presented [1] equation of motion of a reduced density matrix for a system of spins coupled to a second system of spins, the latter being strongly relaxed on account of their coupling to a thermal reservoir, is rederived without recourse to coarse-grained methods. It is shown that the procedure developed here, in contrast to the earlier approach [1], can be extended to corrections of fourth and higher orders in the strength of the coupling between the two groups of spins. The fourth-order terms are presented and applied to the 2A2B3X spin system, the expression derived being compared, for the first-order limit, with the result of an exact calculation. It is shown that the approach [1] becomes invalid in cases for which there is more than one eigenoperator of the Liouville operator appropriate to the rapidly relaxing spins whose eigenvalues are zero or very small. This is shown to occur when the rapidly relaxing group of spins possesses nuclear permutation symmetry and the relaxation of different spins in this group is strongly correlated. An equation of motion of the density matrix is derived for such cases and applied to the 2A3X3Y spin system.