Annihilation of Immobile Reactants on the Bethe Lattice

TL;DR

This paper provides an exact solution for the two-particle annihilation reaction of immobile reactants on the Bethe lattice, revealing exponential concentration decay and extending known one-dimensional results.

Contribution

It offers the first exact solution for immobile reactants on the Bethe lattice and generalizes previous one-dimensional findings to A+B reactions.

Findings

Concentration approaches the limit exponentially.

Reproduces known 1D results.

Extends to A+B reactions.

Abstract

Two-particle annihilation reaction, A+A -> inert, for immobile reactants on the Bethe lattice is solved exactly for the initially random distribution. The process reaches an absorbing state in which no nearest-neighbor reactants are left. The approach of the concentration to the limiting value is exponential. The solution reproduces the known one-dimensional result which is further extended to the reaction A+B -> inert.