  When ions move through solids, they interact with the solid's constituent
atoms and cause them to vibrate around their equilibrium points. This
vibration, in turn, modifies the potential landscape through which the mobile
ions travel. Because the present-time potential depends on past interactions,
the coupling is inherently non-local in time, making its numerical and
analytical treatment challenging. For sufficiently slow-moving ions, we
linearize the phonon spectrum to show that these non-local effects can be
ignored, giving rise to a drag-like force. Unlike the more familiar drag
coefficient in liquids, the drag takes on a matrix form due to the crystalline
structure of the framework. We numerically simulate trajectories and
dissipation rates using both the time-local and non-local formulas to validate
our simplification. The time-local formula dramatically reduces the
computational cost of calculating the motion of mobile particle through a
crystalline framework and clearly connects the properties of the material to
the drag experienced by the particle.
