this competition of disorder and interaction. For $\xi \ll {\mathcal{L}_{\mathrm{n}}}$ ($\xi \gg {\mathcal{L}_{\mathrm{n}}}$) the interaction energy is large (small) as compared to the disorder potential. Due to the fact that the interaction energy increases with increasing density (and $\xi \propto 1/\sqrt{n_0}$), $\xi/{\mathcal{L}_{\mathrm{n}}}$ decreases with increasing density, and disorder effects will fade away in this limit. Thus, for sufficiently high densities an equilibrium condensate will be ordered and superfluid. [@Falco.2009] *Non-equilibrium condensate ii):* In a driven system the mean density $n_0$ of the condensate is determined by a balance of gain and loss. Disorder induces density fluctuations about this mean value. In a region with reduced density, as compared to $n_0$, the gain mechanism tries to compensate the depletion, and more particles are scattered into the condensate than decay. On the other hand, in a region with increased density more particles decay than are injected from the reservoir. By virtue of the continuity equation, these local particle sources and sinks are connected by condensate currents. Because the density fluctuates randomly in space, a random distribution of sources and sinks forms and, thus, a random pattern of current flow is generated. The condensate current is proportional to the product of the density 