@article{MoutalGrebenkov2020,
  author    = {Moutal, Nicolas and Grebenkov, Denis S.},
  title     = {The localization regime in a nutshell},
  series = {Journal of magnetic resonance : JMR},
  volume    = {320},
  journal   = {Journal of magnetic resonance : JMR},
  publisher = {Elsevier},
  address   = {San Diego, Calif. [u.a.]},
  issn      = {1090-7807},
  doi       = {10.1016/j.jmr.2020.106836},
  pages     = {11},
  year      = {2020},
  abstract  = {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 Gaussian form, various models have been employed to interpret these deviations and to relate them with the microstructural properties of a sample. In this paper, we argue that the non-Gaussian behavior of the signal is a generic universal feature of the Bloch-Torrey equation. We provide a simple yet rigorous description of the localization regime emerging at high extended gradients and identify its origin as a symmetry breaking at the reflecting boundary. We compare the consequent non-Gaussian signal decay to other diffusion NMR regimes such as slow-diffusion, motional-narrowing and diffusion-diffraction regimes. We emphasize limitations of conventional perturbative techniques and advocate for non-perturbative approaches which may pave a way to new imaging modalities in this field.},
  language  = {en}
}