Rotatory Brownian motion of a rigid dumbbell

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Abstract
The frictional torque on a dumbbell rotating with time-dependent angular velocity is calculated from the hydrodynamic interaction between the two ends of the dumbbell. This leads to the correlation function for the random torque in rotatory Brownian motion. Although the motion of each dumbbell end has the characteristics of a translational motion, the correlation function at large times decays like t−5/2, as in the case of a solid sphere. The correlation function may be calculated for the limiting case of very small angular displacements. The results for displacements of arbitrary magnitude are the same provided that terms quadratic in the angular velocity are negligible.