  When conducting the numerical simulation of quantum transport, the main
obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The
Quantum Monte Carlo simulation techniques, while being capable of treating the
problems of high dimension, are hindered by the so-called "sign problem". In
the quantum transport, we have fundamental asymmetry between the processes of
emission and absorption of environment excitations: the emitted excitations are
rapidly and irreversibly scattered away. Whereas only a small part of these
excitations is absorbed back by the open subsystem, thus exercising the
non-Markovian self-action of the subsystem onto itself. We were able to devise
a method for the exact simulation of the dominant quantum emission processes,
while taking into account the small backaction effects in an approximate
self-consistent way. Such an approach allows us to efficiently conduct
simulations of real-time dynamics of small quantum subsystems immersed in
non-Markovian bath for large times, reaching the quasistationary regime. As an
example we calculate the spatial quench dynamics of Kondo cloud for a bozonized
Kodno impurity model.
