Diffusion-Limited Coalescence, A+A<-->A, with a Trap

TL;DR

This paper provides an exact solution for diffusion-limited coalescence with a trap in one dimension, revealing how the trap affects the steady state and enabling precise determination of reaction rates.

Contribution

It derives an exact steady-state solution for a one-dimensional diffusion-limited coalescence system with a trap, surpassing traditional approximation methods.

Findings

Exact steady-state solution obtained

Reaction rate coefficients determined precisely

Trap induces a non-equilibrium stationary state

Abstract

We study diffusion-limited coalescence, A+A<-->A$, in one dimension, and derive an exact solution for the steady state in the presence of a trap. Without the trap, the system arrives at an equilibrium state which satisfies detailed balance, and can therefore be analyzed by classical equilibrium methods. The trap introduces an irreversible element, and the stationary state is no longer an equilibrium state. The exact solution is compared to that of a reaction-diffusion equation --- the habitual approximation method of choice. The exact solution allows us to determine the rate coefficients in the reaction-diffusion equation, without appealing to renormalization group techniques.