[@moments]. The system sizes are $L=200$, 400, 800 and 1600 in one dimension, and $L=40$, 80, 160 and 320 in two dimensions.

![[]{data-label="lalb1"}](pb25.eps){width="0.8\hsize"}

![[]{data-label="lalb2"}](lambdaAB.eps){width="0.8\hsize"}

The basic mean-field theory (MFT) (i.e., the one-site approximation), for the 2SCP was derived in [@scp]. Generalized to include different creation rates, $\lambda_A$ and $\lambda_B$, for the two species, and diffusion (nearest-neighbor hopping) of both species at rate $D$, the MFT equations read:

$$\begin{aligned}
\frac{d p_0}{dt} &=& - (\lambda_A \rho_A + \lambda_B \rho_B)p_0 + p_A + p_B
+D[p_A \tilde{\rho}_A + p_B\tilde{\rho}_B - \rho p_0],
\\
\frac{d p_A}{dt} &=&  \lambda_A p_0 \rho_A + \mu p_{AB} - (1 + \lambda_B \rho_B) p_A
+D[p_0\rho_A \!-\! p_A\rho_B +p_{AB}\tilde{\rho}_B \!-\! p_A\tilde{\rho}_A],
\\
\frac{d p_B}{dt} &=&  \lambda_B p_0 \rho_B + \mu p_{AB} - (1 + \lambda_A \rho_A) p_B
+D[p_0\rho_B \!-\! p_B\rho_A +p_{AB}\tilde{\rho}_A \!-\! p_B\tilde{\rho}_B],
\\
\frac{d p_{AB}}{dt} &=& \lambda_B p_A \rho_B + \lambda_A p_B \rho_A - 2 \mu p_{AB}
+D[p_A \rho_B + p_B\rho_A - p_{AB}(2-\rho)],
\label{pab}\end{aligned}$$

where the probabilities for a given site to be vacant, occupied by species A only, by species B only, and doubly occupied are denoted by $p_0$, $p_A$, $p_B$, and $p_{AB}$, respectively, $\rho_A = p_A + p_{AB}$, and $\rho_B = p_B + p_{AB}$. We have further defined 