  We concern the analysis of the long time behavior of interfaces in systems
with two components. Each component evolves according to 1-d Allen-Cahn
equation with Neumann boundary conditions, perturbed by small space-time white
noise and with symmetric double well potential in the interval
$[-\epsilon^{-1},\epsilon^{-1}]$. The two components interact with each other
by an attractive linear force. Instantons are defined as the stationary
solution of the Allen-Cahn equation without noise which connects two pure
phases. We prove that for time $t=\epsilon^{-1}$, in the limit $\epsilon
\rightarrow 0$, when initial states are close to an instanton, two components
stay close to the same instanton, whose center moves as a Brownian motion.
