  Understanding out-of-equilibrium many-body quantum systems is crucial in
contemporary physics. However, capturing the universal dynamics of such systems
remains challenging despite advanced numerical methods. We investigate the
multi-channel Kondo impurity (MCKI) model, hosting an over-screened Kondo state
with non-Fermi liquid characteristics. Using the large-N Schwinger-Keldysh
approach, we study transient dynamics and long-time quasi-equilibrium
properties following a sudden change in the Kondo coupling. We consider two
initial states: over-screened Kondo and high-temperature Fermi liquid. In the
over-screened Kondo state, we observe oscillations in spin-spin correlations
and the Kondo order parameter, representing quantum revival of the entangled
state. In the high-temperature Fermi liquid state, the absence of oscillations
is attributed to the de-phasing mechanism. The system reaches
quasi-equilibrium, manifested as incoherent thermalization between the impurity
and conduction electrons. We observe a non-vanishing effective temperature
difference between the impurity spin (Abrikosov fermion) and the composite
boson formed with conduction electrons at the impurity site. This
quasi-equilibrium is prethermalization, while complete thermalization occurs on
an O(N) timescale with 1/N correction. We discuss the quantum cooling effect
and quantum Boltzmann equations. Our study establishes a foundation for
investigating large-N quantum field theory treatment of quantum many-body
systems, revealing universal properties and a fresh perspective on
prethermalization.
