Langevin dynamics of the elastic dumbbell linked to an adsorbing surface

The overdamped Langevin dynamics of the elastic dumbbell is analyzed introducing moment expansions and deriving exact results for multiple time correlations. In the case of penetrable nonadsorbing surface, the probability of having the oscillator on the same side at a sequence of equally spaced instants of time belonging to a finite interval is expressed as a ratio of multiple integrals. In the limit of very densely distributed observation times, we obtain the analytical expression of this probability related to the unreacted fraction with adsorbing surface. We also give the first correction for small discrete intervals. The calculated unreacted fraction coincides with the diffusion equation result obtained using the Smoluchowski boundary condition. The method, not the result, is potentially extensible to oscillators with inertia. © 1987 The American Physical Society.