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The diffusion motion of spin-bearing molecules is considerably affected in confined environments. In Nuclear Magnetic Resonance (NMR) experiments, under the presence of magnetic field gradients, this movement can be encoded in spin phase…

We consider the generalized Langevin equation (GLE) in a harmonic potential with power law decay memory. We study the anomalous diffusion of the particle's displacement and velocity. By comparison with the free particle situation in which…

The Generalized Langevin Equation (GLE) is a Stochastic Integro-Differential Equation that is commonly used to describe the velocity of microparticles that move randomly in viscoelastic fluids. Such particles commonly exhibit what is known…

We introduce a technique for extracting microstructural geometry from NMR lineshape analysis in porous materials at angstrom-scale resolution with the use of weak magnetic field gradients. Diverging from the generally held view of FID…

When applied to binary solutions, thermal gradients lead to the generation of concentration-gradients and thus to inhomogeneous systems. While being known for more than 150 years, the molecular origins for this phenomenon are still debated,…

Nuclear magnetic resonance (NMR) is a widely used nondestructive method to study random motion of spin-bearing particles in different systems. In the long-time limit the theoretical description of the NMR experiments is well developed and…

We study the relaxation process in normal and anomalous diffusion regimes for systems described by a generalized Langevin equation (GLE). We demonstrate the existence of a very general correlation function which describes the relaxation…

The generalized Langevin equation (GLE) is a universal model for particle velocity in a viscoelastic medium. In this paper, we consider the GLE family with fractional memory kernels. We show that, in the critical regime where the memory…

We model the transport of cosmic ray nuclei in the Galaxy by means of a new numerical code. Differently from previous numerical models we account for a generic spatial distribution of the diffusion coefficient. We found that in the case of…

The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity correlations, and position increments. It…

In the present work, by using the method of accumulation of phase shifts in the rotating frame, the attenuation function S(t) of the NMR signal from an ensemble of spin-bearing particles in a magnetic-field gradient is expressed through the…

Broad theoretical arguments are proposed to show, formally, that the magnitude G of the temperature gradients in turbulent thermal convection at high Rayleigh numbers obeys the same advection-diffusion equation that governs the temperature…

High diffusion-sensitizing magnetic field gradients have been more and more often applied nowadays to achieve a better characterization of the microstructure. As the resulting spin-echo signal significantly deviates from the conventional…

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),…

Understanding diffusion in microstructures plays a crucial role in many scientific fields, including neuroscience, cancer or energy research. While magnetic resonance (MR) methods are the gold standard for diffusion measurements, spatial…

Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time…

The velocity auto-correlation spectra of simple liquids obtained by the NMR method of modulated gradient spin echo show features in the low frequency range up to a few kHz, which can be explained reasonably well by a $t^{-3/2}$ long time…

Distribution functions defined in accord with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet…

Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in…

We consider a generalization of the classical nonrelativistic St\"{o}rmer problem, describing the motion of charged particles in a purely magnetic dipole field, by taking into account the effects of the dissipation, assumed to be of…