because of the rapid changes of density on a microscopic scale. We have to simulate rather large systems in order to identify a macroscopic high(low) density domain by inspection. In Sec. \[sec-expval\] we introduce a numerical method that can detect high and low density domains automatically.

![\[phase\_sep2\] (Colour online) Density profile for $\alpha=0.9$ and $\beta=0.9$ in the disordered TASEP/LK with defect density $\phi=0.2$. One observes phase separation with alternating high and low density domains. The black line displays the density, averaged over 50 adjacent sites.](densprof_dis.eps){width="0.9\columnwidth"}

Theoretical treatment {#sec-theory}
=====================

In this section we develop a theoretical framework for the observations made by Monte Carlo simulations. We expect that concepts developed in this section are generic for a larger class of disordered driven lattice gases that have a single maximum in the current-density relation and weak induced effective interactions between defects. The restriction “weak interaction” is discussed in detail in [@GreulichS08a]. In addition, we assume that the bulk influx term $S(\rho)$ is decreasing with increasing density.

First we summarize the properties that distinguish the inhomogeneous (disordered) TASEP/LK from the TASEP and homogeneous TASEP/LK, respectively.

1.  In the TASEP/LK the particle number is not conserved in the bulk. Therefore generically the current 