  The out of time order correlator (OTOC) serves as a powerful tool for
investigating quantum information spreading and chaos in complex systems. We
present a method employing non-equilibrium dynamical mean-field theory (DMFT)
and coherent potential approximation (CPA) combined with diagrammatic
perturbation on the Schwinger-Keldysh contour to calculate the OTOC for
correlated fermionic systems subjected to both random disorder and electrons
interaction. Our key finding is that random disorder enhances the OTOC decay in
the Hubbard model for the metallic phase in the weak coupling limit. However,
the current limitation of our perturbative solver restricts the applicability
to weak interaction regimes.
