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Langevin Equation in Heterogeneous Landscapes: How to Choose the Interpretation
Adrian Pacheco-Pozo1, Michał Balcerek2, Agnieszka Wyłomanska2
1Department of Electrical and Computer Engineering and School of Biomedical Engineering, <a href="https://ror.org/03k1gpj17">Colorado State University</a>, Fort Collins, Colorado 80523, USA.
Abstract:
The Langevin equation is a common tool to model diffusion at a single-particle level. In nonhomogeneous 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-square displacements. Our analytical results provide a method to choose the interpretation parameter from single-particle tracking experiments.
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