Volume 132, Number 5, December 2020
|Number of page(s)||6|
|Published online||24 February 2021|
Lateral diffusion on a frozen random surface
1 Center for Integrative Medicine and Physics, Institute for Advanced Study, Kyoto University Kyoto 606-8302, Japan
2 Department of Chemistry, Graduate School of Science, Tokyo Metropolitan University Tokyo 192-0397, Japan
Received: 30 September 2020
Accepted: 22 December 2020
The lateral diffusion coefficient of a Brownian particle on a two-dimensional random surface is studied in the quenched limit for which the surface configuration is time independent. We start with the stochastic equation of motion for a Brownian particle on a fluctuating surface, which has been derived by Naji and Brown. The mean square displacement of the particle projected on a base plane is calculated exactly under the condition that the surface with a constant shape has no spatial correlation. We prove that the obtained lateral diffusion coefficient is in between the known upper and lower bounds.
PACS: 05.40.Jc – Brownian motion / 87.16.dp – Transport, including channels, pores, and lateral diffusion / 02.50.Ey – Stochastic processes
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