Hartmann-Hahn Transfer in Multispin Systems

The dynamics of the coherence or polarization transfer is described by so-called transfer functions. Consider an initial density operator 

This definition ensures that for B = A, the transfer function is normalized at the beginning of the mixing time, that is, (0) = 1. If the operator B is Hermitian, that is, if B = B, the transfer function gir) is proportional to the expectation value B (t) = Tr Bo-(T).  

For example, consider the transfer of z magnetization between two spins i and j that are part of a spin system that consists of N spins 1 /2. The amount of z magnetization that is transferred from spin i to spin j as a function of the Hartmann-Hahn mixing time t is given by the transfer function 

If incoherent processes like chemical exchange and relaxation can be disregarded, the transfer function gir) can be written in the form 

For Hermitian operators A and B, the magnitude of the transfer function (t) is limited by the so-called universal bound on spin dynamics (Sprensen, 1989, 1990, 1991)  

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