Condensates in Driven Aggregation Processes

Details Condensates in Driven Aggregation Processes Condensates in Driven Aggregation Processes

2006-08-23

arxiv.org/abs/cond-mat/0608519v1

Phys. Rev. E 75, 011103 (2007)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 3 figures

Scientific paper

10.1103/PhysRevE.75.011103

We investigate aggregation driven by mass injection. In this stochastic process, mass is added with constant rate r and clusters merge at a constant total rate 1, so that both the total number of clusters and the total mass steadily grow with time. Analytic results are presented for the three classic aggregation rates K_{i,j} between clusters of size i and j. When K_{i,j}=const, the cluster size distribution decays exponentially. When K_{i,j} (i+j) or K_{i,j} (ij), there are two phases: (i) a condensate phase with a condensate containing a finite fraction of the mass in the system as well as finite clusters, and (ii) a cluster phase with finite clusters only. For K_{i,j} (i+j), the cluster size distribution, c_k, has a power-law tail, c_k~k^{-gamma} in either phase. The exponent is a non-monotonic function of the injection rate: gamma=r/(r-1) in the condensate phase, r<2, and \gamma=r in the cluster phase, r>2.

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