Abstract
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.
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