Dynamic condensates in aggregation processes with mass injection

Abstract

The Takayasu aggregation model is a paradigmatic model of aggregation with mass injection, known to exhibit a power law distribution of mass over a range which grows in time. Working in one dimension we find that the mass profile in addition shows distinctive {\it dynamic condensates} which collectively hold a substantial portion of the mass (approximately $80\%$ when injection and diffusion rates are equal) and lead to a substantial hump in the scaled distribution. To track these, we monitor the largest mass within a growing coarsening length. An interesting outcome of extremal statistics is that the mean of the globally largest mass in a finite system grows as a power law in time, modulated by strong multiplicative logarithms in both time and system size. At very long times in a finite system, the state consists of a power-law-distributed background with a condensate whose mass increases linearly with time.