DIFFUSION-CONTROLLED INITIAL RECOMBINATION

This work addresses nucleation rates in systems with strong initial re combination. Initial (or ''geminate'') recombination is a process wher e a dissociated structure (anion, vortex, kink, etc.) recombines with its twin brother (cation, antivortex, antikink) generated in the same nucleation event. Initial recombination is important if there is an as ymptotically vanishing interaction force instead of a generic saddle-t ype activation barrier. At low temperatures, initial recombination str ongly dominates homogeneous recombination. In a first part, we discuss the effect in one-, two-, and three-dimensional diffusion controlled systems with spherical symmetry. Since there is no well-defined saddle , we introduce a threshold which is to some extent arbitrary but which is restricted by physically reasonable conditions. We show that the d ependence of the nucleation rate on the specific choice of this thresh old is strongest for one-dimensional systems and decreases in higher d imensions. We also discuss the influence of a weak driving force, and show that the transport current is directly determined by the imbalanc e of the activation rate in the direction of the field and the rate ag ainst this direction. In a second part, we apply the results to the ov erdamped sine-Gordon system at equilibrium. It turns out that diffusiv e initial recombination is the essential mechanism which governs the e quilibrium kink nucleation rate. We emphasize analogies between the si ngle particle problem with initial recombination and the multidimensio nal kink-antikink nucleation problem.