  The dynamic scaling properties of the one dimensional Burgers equation are
expected to change with the inclusion of additional conserved degrees of
freedom. We study this by means of 1-D driven lattice gas models that conserve
both mass and momentum. The most elementary version of this is the
Arndt-Heinzel-Rittenberg (AHR) process, which is usually presented as a two
species diffusion process, with particles of opposite charge hopping in
opposite directions and with a variable passing probability.
  From the hydrodynamics perspective this can be viewed as two coupled Burgers
equations, with the number of positive and negative momentum quanta
individually conserved. We determine the dynamic scaling dimension of the AHR
process from the time evolution of the two-point correlation functions, and
find numerically that the dynamic critical exponent is consistent with simple
Kardar-Parisi-Zhang (KPZ) type scaling. We establish that this is the result of
perfect screening of fluctuations in the stationary state. The two-point
correlations decay exponentially in our simulations and in such a manner that
in terms of quasi-particles, fluctuations fully screen each other at coarse
grained length scales. We prove this screening rigorously using the analytic
matrix product structure of the stationary state. The proof suggests the
existence of a topological invariant. The process remains in the KPZ
universality class but only in the sense of a factorization, as $({KPZ})^2$.
The two Burgers equations decouple at large length scales due to the perfect
screening.
