Theory of quantum dipole-dipole relaxation of magnetic resonance signal in low-dimensional systems

The role of quantum dipole-dipole interactions in formation of the magnetic resonance signal is analyzed in two- and one-dimension systems. The theory predicts magnetic field and orientational dependence of spin-lattice (i.e., longitudinal T1) and spin-spin (i.e., transverse T2) relaxation parameters. In contrast to the 3D model, the transverse relaxation in the low-dimensional models cannot be described in terms of a standard R2 = 1/T2 relaxation rate parameter, but by an anisotropic apparent relaxation rate function R2(t) depending on time t after RF excitation. In the main approximation, R2(t, α) ∼ ln t in the 2D model, and R2(t) ∼ t1/2 in the 1D model.