Abstract of the poster "An exactly solvable model for restricted diffusion in NMR"
Diffusive transport of spin-bearing particles in a geometrical
confinement can be monitored by applying inhomogeneous magnetic
fields to "encode" their trajectories through variable dephasing
of the spins. Since the macroscopic signal is proportional to
the characteristic function of this dephasing, useful information
about diffusive transport and confining geometry can be extracted
from experimental measurements. However, the analysis was in general
limited to the second order moment, known as "Gaussian phase
approximation" (GPA).
We propose an exactly solvable model by considering restricted
diffusion between parallel planes in a cosine magnetic field.
The specific choice of this spatial profile as proportional to an
eigenfunction of the Laplace operator in this confining geometry
considerably simplifies the underlying mathematics. In particular,
exact and explicit relations for several moments of the dephasing
are derived. These relations are shown to provide good approximations
for the typical case of a linear magnetic field gradient. We study
the structure and the properties of the higher order moments which
are responsible for the breakdown of the GPA at intense magnetic fields.
A diagram of different restricted diffusion regimes is presented.
Keywords: restricted diffusion, confinement, solvable model, NMR, Laplace operator eigenfunctions