Long-Range and Many-Body Effects in Coagulation Processes

TL;DR

This paper investigates the effects of long-range interactions and many-body fluctuations on coagulation processes, revealing deviations from classical decay laws through a non-perturbative renormalization group analysis.

Contribution

It provides an exact mapping from microscopic details to macroscopic decay rates and identifies a universal correction term due to long-range and many-particle effects.

Findings

Anomalously slow decay below the critical dimension two.

Confirmation of the law of mass action above two dimensions.

Discovery of a universal correction term violating classical decay laws.

Abstract

We study the problem of diffusing particles which coalesce upon contact. With the aid of a non-perturbative renormalization group, we first analyze the dynamics emerging below the critical dimension two, where strong fluctuations imply anomalously slow decay. Above two dimensions, the long-time, low-density behavior is known to conform with the law of mass action. For this case, we establish an exact mapping between the physics at the microscopic scale (lattice structure, particle shape and size) and the macroscopic decay rate in the law of mass action. In addition, we identify a term violating this classical law. It originates in long-range and many-particle fluctuations and is a simple, universal function of the macroscopic decay rate.