title: Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory.
abstract: The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.
authors.affiliation: Department of Physics, Technical University of Košice, Park Komenského 2, 042 00 Košice, Slovakia; Laboratory of Radiation Biology, Joint Institute of Nuclear Research, 141 980 Dubna, Moscow Region, Russia. Electronic address: vladimir.lisy@tuke.sk.
authors.forename: Vladimír
authors.initials: V
authors.lastname: Lisý
authors.affiliation: Department of Physics, Technical University of Košice, Park Komenského 2, 042 00 Košice, Slovakia.
authors.forename: Jana
authors.initials: J
authors.lastname: Tóthová
keywords: Brownian motion; Diffusion; Generalized Langevin equation; Induction signal; NMR; Spin echo