Critical properties of cluster size distribution in an asymmetric diffusion-aggregation model

International audienceWe consider a stochastic dynamics for a system of diffusing hard-core particles on a periodic chain with asymmetric diffusion rules. A given cluster of particles can diffuse to the right as a whole but the particle located on the left boundary of the cluster is allowed to break off from it and diffuse to the left. Clusters of particles can eventually merge with other clusters. These rules allow for the creation of clusters of different sizes. We discuss the size distribution of the clusters in the long time or steady state limit, as a function of the particle concentration c. We consider the general time dependent master equation based on Smoluchowski's theory for local cluster merging or fragmentation and diffusion processes, and study the solutions using the generating function in the large size limit. We found that there exists a critical density c∗ =√2 − 1 for which the cluster distribution decays like a power law with exponent 5/