Transport and fluctuations in mass aggregation processes: mobility driven clustering

TL;DR

This paper investigates mass aggregation processes on a ring, revealing a mobility-driven clustering transition linked to diverging conductivity and mass fluctuations, akin to a superfluid-like phase transition.

Contribution

It provides an analytical study of diffusion, conductivity, and clustering in mass aggregation models, highlighting the role of mobility and a condensation transition without microscopic reversibility.

Findings

Conductivity diverges at a critical density, indicating a phase transition.

Mass fluctuations increase with enhanced mobility, leading to clustering.

Bulk-diffusion coefficient remains finite across regimes.

Abstract

We calculate the bulk-diffusion coefficient and the conductivity in a broad class of conserved-mass aggregation processes on a ring of discrete sites. These processes involve chipping and fragmentation of masses, which diffuse around and aggregate upon contact with their neighboring masses. We find that, even in the absence of microscopic time reversibility, the systems satisfy an Einstein relation, which connects the ratio of the conductivity and the bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation dominates over chipping, the conductivity or, equivalently, the mobility, gets enhanced. The enhancement in conductivity, in accordance with the Einstein relation, results in large mass fluctuations, implying a {\it mobility driven clustering} in the system. Indeed, in a certain parameter regime, we demonstrate that the conductivity diverges beyond a critical density, signaling the onset of a condensation transition observed in the past. In a striking similarity to Bose-Einstein condensation, the condensate formation along with the diverging conductivity thus underlies a dynamic "superfluidlike" transition in these nonequilibrium systems. Notably, the bulk-diffusion coefficient remains finite in all cases. Our analytic results are in a quite good agreement with simulations.