Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly...

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Bibliographic Details
Main Authors: Lisý, Vladimír, Tóthová, Jana
Format: Conference Proceeding
Language:English
Subjects:
Attenuation
Brownian motion
Mathematical models
NMR
Nuclear magnetic resonance
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Summary:Nuclear magnetic resonance is often used to study random motion of spins in different systems. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S ( t ) for an ensemble of spins in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in a simple way and used for the calculation of S ( t ). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues.
ISSN:2100-014X
2101-6275
2100-014X
DOI:10.1051/epjconf/201817302013