Numerical Simulation of the Trapping Reaction with Mobile and Reacting Traps

TL;DR

This paper investigates a complex two-species diffusion reaction system, confirming theoretical predictions of anomalous decay behavior through advanced computer simulations that improve statistical accuracy.

Contribution

The authors develop a novel simulation method to accurately measure the probability distribution in a reaction-diffusion system, validating renormalization group predictions.

Findings

Confirmed the anomalous dimension predicted by RG methods.

Achieved high-precision numerical results matching theoretical values.

Demonstrated the effectiveness of the new simulation technique.

Abstract

We study a variation of the trapping reaction, A+B->A, in which both the traps (A) and the particles (B) undergo diffusion, and the traps upon meeting react according to A+A->0 or A. This two-species reaction-diffusion system is known to exhibit a non-trivial decay exponent for the B particles, and recently renormalization group methods have predicted an anomalous dimension in the BB correlation function. To test these predictions we develop a computer simulation method, motivated by the technique of Mehra and Grassberger, that determines the complete probability distribution of the B particles for a given realization of the A particle dynamics, thus providing a significant increase the quality of statistics. Our numerical results indeed reveal the anomalous dimension predicted by the renormalization group, and compare well quantitatively to precisely known values in cases where the problem can be related to a 4-walker problem.