Nuclear Induction Lineshape: Non-Markovian Diffusion with Boundaries

The dynamics of viscoelastic fluids are described by a memory function, the computation of which can be challenging in scenarios involving boundaries to diffusion. Herein we present an approach to effectively capture the memory effects through the time-correlation function of the pressure tensor, or viscosity. This is accomplished by employing a frequency-dependent Stokes-Einstein equation, leveraging inputs derived from molecular dynamics simulations. We show how to compute NMR lineshape using a generalized diffusion coefficient that accounts for temperature variations and pore size. This new framework, which connects memory function to the thermal transport parameter, provides a direct way to compute NMR signals of non-Markovian fluids in the presence of boundaries to diffusion.