\[fig:2nd\]b) that the overall redistribution of particles is from high $k$ to small $k$, which means that the Beliaev decay of high-momentum quasiparticles is dominant. Around the two extremal momenta of the input states, $q_\text{min}$ and $q_\text{max}$, this manifests itself as a peak in the momentum distribution, while there is a dip at the extremal momenta $k_\text{min}$ and $k_\text{max}$ of the output states. This is a consequence of the relatively large density of states for possible output (input) states for scatterings with input (output) momenta around $k_\text{min}$ or $k_\text{max}$ ($q_\text{min}$ or $q_\text{max}$), as one can deduce in Fig.\[fig:bel\_decay\]b from the slow bending of the contours at these extremal values. As energy does not need to be exactly conserved in an open system, scattering is also possible slightly outside the interval $[q_\text{min},k_\text{max}]$, with a width set by the linewidth $\gamma$. This characteristic series of peaks and dips in the steady-state momentum distribution appears to be a promising experimental signature of Beliaev-Landau scattering processes in a novel context of non-equilibrium quantum fluids. On the other hand, in the limit of small and large momenta ($k \rightarrow 0$ and $k \rightarrow \pi$) Beliaev-Landau processes are not allowed, so the Bogoliubov result is accurately 