  We present a numerical method for studying the real time dynamics of a small
interacting quantum system coupled to an infinite fermionic reservoir. By
building an orthonormal basis in the operator space, we turn the Heisenberg
equation of motion into a system of linear differential equations, which is
then solved iteratively by constructing excitation operators. The application
of our method depends on a layer structure in the operator space, which help us
to turn an infinite linear system into a series of small systems. We apply the
method to investigate the decoherence dynamics of quantum impurity models in
the Kondo regime with a non-Markovian reservoir. Taking full account of
environmental back-actions and electron-electron interactions, we find that the
coexistence of the Kondo correlation and a non-Markovian reservoir induces
coherence ringings, which will be suppressed by either driving the system away
from the particle-hole symmetric point or changing the reservoir into a
Markovian one.
