%0 Book Section %1 statphys23_0291 %A Grebenkov, D.S. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K confinement diffusion eigenfunctions laplace model nmr operator restricted solvable statphys23 topic-3 %T An exactly solvable model for restricted diffusion in NMR %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=291 %X 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.

@incollection{statphys23_0291, abstract = {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.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Grebenkov, D.S.}, biburl = {https://www.bibsonomy.org/bibtex/2441065560f91a032003e8d3f4b1dc88e/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0a4f75d8f4eab2c5dba7ea961b28b52c}, intrahash = {441065560f91a032003e8d3f4b1dc88e}, keywords = {confinement diffusion eigenfunctions laplace model nmr operator restricted solvable statphys23 topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:16.000+0200}, title = {An exactly solvable model for restricted diffusion in NMR}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=291}, year = 2007 }