  The equilibrium physics of quantum impurities frequently involves a universal
crossover from weak to strong reservoir-impurity coupling, characterized by
single-parameter scaling and an energy scale $T_K$ (Kondo temperature) that
breaks scale invariance. For the non-interacting resonant level model, the
non-equilibrium time evolution of the Loschmidt echo after a local quantum
quench was recently computed explicitely [R. Vasseur, K. Trinh, S. Haas, and H.
Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling
with variable $T_K t$. Here, we scrutinize whether similar universal dynamics
can be observed in various interacting quantum impurity systems. Using density
matrix and functional renormalization group approaches, we analyze the time
evolution resulting from abruptly coupling two non-interacting Fermi or
interacting Luttinger liquid leads via a quantum dot or a direct link. We also
consider the case of a single Luttinger liquid lead suddenly coupled to a
quantum dot. We investigate whether the field theory predictions for the
universal scaling as well as for the large time behavior successfully describe
the time evolution of the Loschmidt echo and the entanglement entropy of
microscopic models.
