A DUMBBELLS RANDOM-WALK IN CONTINUOUS-TIME

We study the continuous-time dynamics of a rigid dumbbell or, equivalently, of two random walkers coupled through a holonomic constraint. Random walkers under holonomic constraints provide a generic model for many physical systems, e.g. for polymers. Interestingly, the spatial and temporal aspects of the dumbbell's motion are highly coupled: the ensuing behaviour differs considerably from a simple continuous-time random walk (CTRW)-picture. For waiting-time distributions with broad probability densities the dumbbell's dynamics parallels that of polymers in melts, in that two diffusive regimes appear, connected by a broad crossover region. We determine analytically the diffusion constants in the two regimes from a higher-order decoupling approach; the results agree well with simulations.