We introduce an extension of the nonequilibrium dynamical mean-field theory to incorporate the effects of static random disorder in the dynamics of a many-particle system by integrating out different disorder configurations resulting in an effective time-dependent density-density interaction. We use this method to study the nonequilibrium transient dynamics of a system described by the Fermi Anderson-Hubbard model following an interaction and disorder quench. The method recovers the solution of the disorder-free case for which the system exhibits qualitatively distinct dynamical behaviors in the weak-coupling (prethermalization) and strong-coupling regimes (collapse-and-revival oscillations). However, we find that weak random disorder promotes thermalization. In the weak-coupling regime, the jump in the quasiparticle weight in the prethermal regime is suppressed by random disorder, while in the strong-coupling regime, random disorder reduces the amplitude of the quasiparticle weight oscillations. These results highlight the importance of disorder in the dynamics of realistic many-particle systems.

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• Disordered systems
• Nonequilibrium systems
• Strongly correlated systems
• Dynamical mean field theory