Dynamic condensates in aggregation processes

The Takayasu aggregation model is a model of aggregation with mass injection, known to exhibit a power law distribution of mass $\sim \frac{1}{m^\tau}$ with $\tau = \frac{4}{3}$ in 1D, over a mass range which grows in time. It is a paradigmatic model in non-equilibrium statistical physics, having exact correspondences with models of river basins, granular stackings, spanning trees and the voter model.

We find that in addition to the power law, the system has distinctive dynamic condensates which hold a substantial portion of the mass, leading to a distinctive hump in the scaled distribution. In the long-time state in a closed finite system, there is a single condensate whose mass increases linearly with time while the rest of the system reaches a stationary state. The diffusing condensate acts like a forager which reconfigures the rest of the system in an interesting fashion. For instance, on sites close to the condensate, we show that the mass distribution power law changes to $\tau=\frac{5}{3}$ different from the value $\frac{4}{3}$ in the bulk.

These steady state results also imply anomalies in mass distributions during the evolution of the model in time, verified by simulations.

[Work done in collaboration with Arghya Das, Reya Negi and Rajiv Pereira]