  We study non-equilibrium dynamics and quantum quenches in a recent
gauge/gravity duality model for a strongly coupled system interacting with a
magnetic impurity with $SU(N)$ spin. At large $N$, it is convenient to write
the impurity spin as a bilinear in Abrikosov fermions. The model describes an
RG flow triggered by the marginally relevant Kondo operator. There is a phase
transition at a critical temperature, below which an operator condenses which
involves both an electron and an Abrikosov fermion field. This corresponds to a
holographic superconductor in AdS$_2$ and models the impurity screening. We
study the time dependence of the condensate induced by quenches of the Kondo
coupling. The timescale for equilibration is generically given by the
lowest-lying quasinormal mode of the dual gravity model. This mode also governs
the formation of the screening cloud, which is obtained as the decrease of
impurity degrees of freedom with time. In the condensed phase, the leading
quasinormal mode is imaginary and the relaxation of the condensate is
over-damped. For quenches whose final state is close to the critical point of
the large $N$ phase transition, we study the critical slowing down and obtain
the combination of critical exponents $z\nu=1$. When the final state is exactly
at the phase transition, we find that the exponential ringing of the
quasinormal modes is replaced by a power-law behaviour of the form $\sim
t^{-a}\sin(b\log t)$. This indicates the emergence of a discrete scale
invariance.
