  The coherent transport of $n$ fermions in disordered networks of $l$ single-particle states connected by $k$-body interactions is studied. These networks are modeled by embedded Gaussian random matrix ensemble (EGE). The conductance bandwidth as well as the ensemble-averaged total current attain their maximal values if the system is highly filled $n \sim l-1$ and $k\sim n/2$. For the cases $k=1$ and $k=n$ the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever centrosymmetric ensemble (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and thus, causes backscattering-free transmission resonances which enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak for $n=l-1$, close to the highest observed currents. 
Efficient quantum transport in disordered interacting many-body networks