Transverse spin relaxation in inhomogeneous magnetic fields

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Abstract
We discuss the transition between two limiting cases of transverse spin relaxation due to magnetic-field inhomogeneities: very fast spatial diffusion, when the spins relax exponentially with time, and very slow spatial diffusion, when the spins relax exponentially with the cube of the time. Both limiting cases as well as intermediate cases can be described in terms of Airy functions, which are the eigenfunctions of the time-independent Torrey equation. Branch points in the eigenvalue spectrum and other interesting properties follow from the fact that the Torrey equation is not self-adjoint.