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We present a rigorous framework to obtain evolution equations for themomentum distribution and higher order correlation functions in weaklyinteracting systems based on the Projection Operator Technique. These equationscan be numerically solved in an efficient way. We compare the solution of theequations with known results for 1D models and find an excellent agreement.

Equations of Motion for the Out-of-Equilibrium Dynamics of Isolated Quantum Systems from the Projection Operator Technique