  We prove that the variance of the current across a characteristic is of order
t^{2/3} in a stationary constant rate totally asymmetric zero range process,
and that the diffusivity has order t^{1/3}. This is a step towards proving
universality of this scaling behavior in the class of one-dimensional
interacting systems with one conserved quantity and concave hydrodynamic flux.
The proof proceeds via couplings to show the corresponding moment bounds for a
second class particle. We build on the methods developed by Balazs-Seppalainen
for asymmetric simple exclusion. However, some modifications were needed to
handle the larger state space. Our results translate into t^{2/3}-order of
variance of the tagged particle on the characteristics of totally asymmetric
simple exclusion.
