The Master Equation of Relaxation

The evolution of the density operator is described by Eq. (2.10). Thus far the spin Hamiltonian in this equation has been considered to be static or time-independent. A spin system with the Hamiltonian given by 

Writing a and as a and in the interaction representation isolates the effect of the spin-lattice coupling, since Eq. (5.2) becomes 

Its average over all identical molecules is taken in the sample, which is identical to its time average for any given molecule. The average is represented by a bar in the following equation  

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When this is used in conjunction with Eq. (5.3), it represents the solution to the master equation of relaxation. If the spin-lattice couplings fluctuate slowly, treatment of spin relaxation in the slow motion regime requires solving the stochastic Liouville equation [5.6]. 

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