Langevin equation in heterogeneous landscapes: how to choose the interpretation

Adrian Pacheco-Pozo, Michał Balcerek, Agnieszka Wyłomańska, Krzysztof Burnecki, Igor M. Sokolov, Diego Krapf

Published 2024-03-18, updated 2024-06-18Version 2

The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases, the solution to a Langevin equation is not unique unless the interpretation of stochastic integrals involved is selected. We analyze the diffusion of particles in such systems and evaluate the mean, the mean square displacement, and the distribution of particles, as well as the variance of the time-averaged mean-squared displacements. Our analytical results provide a method to choose the interpretation parameter from single particle tracking experiments.