Analytical correlation functions for motion through diffusivity landscapes.

Diffusion of a particle through an energy and diffusivity landscape is a very general phenomenon in numerous systems of soft and condensed matter. On the one hand, theoretical frameworks such as Langevin and Fokker-Planck equations present valuable accounts to understand these motions in great detail, and numerous studies have exploited these approaches. On the other hand, analytical solutions for correlation functions, as, e.g., desired by experimentalists for data fitting, are only available for special cases. We explore the possibility to use different theoretical methods in the specific picture of time-dependent switching between diffusive states to derive analytical functions that allow to link experimental and simulation results to theoretical calculations. In particular, we present a closed formula for diffusion switching between two states, as well as a general recipe of how to generalize the formula to multiple states.