  We consider the totally asymmetric simple exclusion processes on quenched
random energy landscapes. We show that the current and the diffusion
coefficient differ from those for homogeneous environments. Using the
mean-field approximation, we analytically obtain the site density when the
particle density is low or high. As a result, the current and the diffusion
coefficient are described by the dilute limit of particles or holes,
respectively. However, in the intermediate regime, due to the many-body effect,
the current and the diffusion coefficient differ from those for single-particle
dynamics. The current is almost constant and becomes the maximal value in the
intermediate regime. Moreover, the diffusion coefficient decreases with the
particle density in the intermediate regime. We obtain analytical expressions
for the maximal current and the diffusion coefficient based on the renewal
theory. The deepest energy depth plays a central role in determining the
maximal current and the diffusion coefficient. As a result, the maximal current
and the diffusion coefficient depend crucially on the disorder, i.e.,
non-self-averaging. Based on the extreme value theory, we find that
sample-to-sample fluctuations of the maximal current and diffusion coefficient
are characterized by the Weibull distribution. We show that the disorder
averages of the maximal current and the diffusion coefficient converge to zero
as the system size is increased and quantify the degree of the
non-self-averaging effect for the maximal current and the diffusion
coefficient.
