Heuristic Approach to Trajectory Correlation Functions in Bounded Regions with Lambert Scattering Walls

The behavior of spins undergoing Larmor precession in the presence of time varying fields is of interest to many research fields. The frequency shifts and relaxation resulting from these fields are related to their power spectrum, determined from the Fourier Transform of the auto-correlation functions of the time varying field. Using the method of images C. M. Swank, A. K. Petukhov, and R. Golub (2012 and 2016) calculated the position-position auto-correlation function for particles moving in a rectangular cell with specular scattering walls. In this work we present a heuristic model that applies the method of images to the case of Lambert scattering walls. The results of this model are compared to simulation and show remarkably good agreement from the ballistic to diffusive regime of gas collisions, for both square and general rectangular cells.