  Critical properties of the dynamical phase transition in the quenched
generalized Bose-Anderson impurity model are studied in the mean-field limit of
an infinite number of channels. The transition separates the evolution toward
ground state and toward the branch of stable excited states. We perform
numerically exact simulations of a close vicinity of the critical quench
amplitude. The relaxation constant describing the asymptotic evolution toward
ground state, as well as asymptotic frequency of persistent phase rotation and
number of cloud particles at stable excited state are power functions of the
detuning from the critical quench amplitude. The critical evolution (separatrix
between the two regimes) shows a non-Lyapunov power-law instability arising
after a certain critical time. The observed critical behavior is attributed to
the irreversibility of the dynamics of particles leaving the cloud and to
memory effects related to the low-energy behavior of the lattice density of
states.
