Fluctuations in the motions of mass and of patterns in one-dimensional driven diffusive systems

The stochastic spreading of mass fluctuations in systems described by a fluctuating Burgers equation increases ast2/3 with time. As a consequence the stochastic motion of a mass front, a point through which no excess mass current is flowing, is shown to increase ast1/3. The same is true for the stochastic displacement of mass points and shock fronts with respect to their average drift, provided the initial configuration is fixed. An additional average over the stationary distribution of the initial configuration yields stochastic displacements, increasing with time ast1/2.