we have simulated disordered systems with small but finite defect density $\phi$ for small $\alpha$ and large $\beta$. In contrast to systems with few defects, the current profile of the disordered system differs from the that of the homogeneous system. This is due to the change of the density by defects, which leads to an altered influx of particles in the bulk by attachment/detachment. So the gradient of the current profile in the disordered system is different from the one in the homogeneous system and also from the system with few defects because in the latter the effect on the average density is negligible.

![\[LD-profs2\](Colour online) Comparison of current and density profiles for $\alpha=0.1$ and $\beta=0.9$ (low density phase) in the disordered TASEP/LK with defect density $\phi=0.1$ and homogeneous TASEP/LK.](DP_LD_dis.eps "fig:"){width="0.9\columnwidth"}\
![\[LD-profs2\](Colour online) Comparison of current and density profiles for $\alpha=0.1$ and $\beta=0.9$ (low density phase) in the disordered TASEP/LK with defect density $\phi=0.1$ and homogeneous TASEP/LK.](Jprofs_LD_dis.eps "fig:"){width="0.9\columnwidth"}

Like in the TASEP/LK with few defects we observe multiple high and low density domains for large boundary rates, which is displayed in Fig.  \[phase\_sep2\]. In fact it is harder to distinguish macroscopic high and low density regimes in the disordered case 