CS13: Complex Systems I

Organizer: Krzysztof Burnecki (Wrocław University of Science and Technology)

Langevin equation in quenched heterogeneous landscapes

Diego Krapf

The Langevin equation is a common tool to model diffusion at the 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 analyse 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 \([1]\). We provide solutions as a function of the interpretation parameter \(\alpha\), with particular attention to the Itô, Stratonovich, and Hänggi-Klimontovich interpretations, revealing fundamentally different behaviours. Furthermore, heterogeneous diffusion is also considered when the particle is subjected to an external force. Our analytical results provide a method to choose the interpretation parameter from single particle tracking experiments.

Bibliography

\([1]\) A. Pacheco-Pozo, M. Balcerek, A. Wyłomańska, K. Burnecki, I.M. Sokolov, and D. Krapf. "Langevin equation in heterogeneous landscapes: how to choose the interpretation." Phys. Rev. Lett. , vol. 133, 2024, pp. 067102.