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Understanding out-of-equilibrium many-body quantum systems is crucial incontemporary physics. However, capturing the universal dynamics of such systemsremains challenging despite advanced numerical methods. We investigate themulti-channel Kondo impurity (MCKI) model, hosting an over-screened Kondo statewith non-Fermi liquid characteristics. Using the large-N Schwinger-Keldyshapproach, we study transient dynamics and long-time quasi-equilibriumproperties following a sudden change in the Kondo coupling. We consider twoinitial states: over-screened Kondo and high-temperature Fermi liquid. In theover-screened Kondo state, we observe oscillations in spin-spin correlationsand the Kondo order parameter, representing quantum revival of the entangledstate. In the high-temperature Fermi liquid state, the absence of oscillationsis attributed to the de-phasing mechanism. The system reachesquasi-equilibrium, manifested as incoherent thermalization between the impurityand conduction electrons. We observe a non-vanishing effective temperaturedifference between the impurity spin (Abrikosov fermion) and the compositeboson formed with conduction electrons at the impurity site. Thisquasi-equilibrium is prethermalization, while complete thermalization occurs onan O(N) timescale with 1/N correction. We discuss the quantum cooling effectand quantum Boltzmann equations. Our study establishes a foundation forinvestigating large-N quantum field theory treatment of quantum many-bodysystems, revealing universal properties and a fresh perspective onprethermalization.

Prethermalization and transient dynamics of the Multi-Channel Kondo  systems under generic quantum quenches: Insights form Large-$N$  Schwinger-Keldysh approach