Fast-diffusion mean-field theory for k-body reactions in one dimension

TL;DR

This paper introduces an improved mean-field approximation for k-body annihilation reactions of hard-core diffusing particles on a line, enhancing accuracy especially for large k values by accounting for particle properties.

Contribution

The paper develops a new mean-field theory that better models k-body reactions in one dimension, extending applicability beyond standard chemical rate equations.

Findings

The new theory accurately predicts reaction dynamics for k=3 to 6.

It has a larger validity region than traditional models.

Numerical tests confirm improved performance for large k.

Abstract

We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation processes are correlated to mimic chemical reactions. Our new mean-field theory accounts for hard-core particle properties and has a larger region of applicability than the standard chemical rate equation especially for large k values. Criteria for validity of the mean-field theory and its use in phenomenological data fits are derived. Numerical tests are reported for k=3,4,5,6.