Redfield-type theory

Zheng et al derived a Redfield-type theory for magnetic field gradient-induced relaxation of spins undergoing restricted diffusion. The theory covered both transverse and longitudinal relaxation and the approach was valid in all diffusion regimes. The theory can be useful for MRI in structured media and was illustrated with experiments on gaseous, polarized He. 

On less formal grounds a Markovian type of equation was also obtained by Redfield [167]. Redheld used perturbation theory up to second order and derived a Master equation for the evolution of the density matrix Oaa y where a, a denote quantum states of the molecule with energy defined by ha. The simple equation for the relaxation of the density matrix was obtained by neglecting the ensemble-averaged first-order terms. Thus we have [167]... 

In the frame of the Bloch/Wangsness/Redfield (BWR) relaxation theory [2, 17], the fluctuations of the spin Hamiltonians are described with the aid of (preferably normalized) autocorrelation functions of the type... 

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