The A+B -> 0 annihilation reaction in a quenched random velocity field

TL;DR

This paper investigates the long-time decay of the A+B -> 0 reaction in a quenched random velocity field using renormalization group methods, revealing universal decay laws dependent on spatial dimensions.

Contribution

It introduces a field-theoretic approach to analyze the reaction in a quenched velocity field, deriving universal decay exponents and amplitudes for arbitrary dimensions.

Findings

Density decays as t^{-(d+3)/8} for d<3

Universal amplitude A calculated at first order in epsilon

Velocity field modeled with short-range correlations in perpendicular directions

Abstract

Using field-theoretic renormalization group methods the long-time behaviour of the A+B -> 0 annihilation reaction with equal initial densities n_A(0) = n_B(0) = n_0 in a quenched random velocity field is studied. At every point (x, y) of a d-dimensional system the velocity v is parallel or antiparallel to the x-axis and depends on the coordinates perpendicular to the flow. Assuming that v(y) have zero mean and short-range correlations in the y-direction we show that the densities decay asymptotically as n(t) ~ A n_0^(1/2) t^(-(d+3)/8) for d<3. The universal amplitude A is calculated at first order in \epsilon = 3-d.