Proton and Deuteron Field-Cycling NMR Relaxometry of Liquids in Porous Glasses: Evidence for Lévy-Walk Statistics

${}^1\mathrm{H}$ and ${}^2\mathrm{H}$ field-cycling NMR relaxometry of polar and nonpolar liquids in porous glasses (4 and 30 nm pores) shows pronounced differences of the spin-lattice relaxation dispersion for “weak” (nonpolar) and “strong” (polar) adsorption. In the latter case bulk-mediated surface diffusion was predicted so that Lévy walks with a Cauchy propagator follow [Bychuk et al., Phys. Rev. Lett. 74, 1795 (1995)]. The data can be perfectly interpreted by this mechanism in combination with reorientations mediated by translational displacements. The evaluated surface correlation functions are characterized by correlation lengths in the same order as the pore diameters.