Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input

TL;DR

This paper analyzes the stationary states of a one-dimensional coagulation-diffusion model with external input, revealing universal concentration behaviors depending on diffusion symmetry and highlighting surprising universality in asymmetric cases.

Contribution

It provides analytical and numerical evidence for universal concentration profiles in a coagulation-diffusion system with external input, including asymmetric diffusion scenarios.

Findings

Concentration decays as 1/x with symmetric diffusion.

Concentration decays as 1/√x with asymmetric diffusion.

The universality of the constant Aa is observed despite a massive spectrum.

Abstract

We investigate with the help of analytical and numerical methods the reaction A+A->A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for large x, the particle concentration c(x) behaves like As/x (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction the particle concentration behaves like Aa/sqrt(x). The constants As and Aa are independent of the input and the two coagulation rates. The universality of Aa comes as a surprise since in the asymmetric case the system has a massive spectrum.