  A new approach to the theory and simulation of the non-Markovian dynamics of
open quantum systems is presented. It is based on identification of a parameter
which is uniformly small on wide time intervals: the occupation of the virtual
cloud of quanta. By "virtual" we denote those bath excitations which were
emitted by the system, but eventually will be reabsorbed before any measurement
of the bath state. A favourable property of the virtual cloud is that the
number of its quanta is expected to saturate on long times, since physically
this cloud is a (retarded) polarization of the bath around the system.
Therefore, the joint state of open system and of virtual cloud (the dressed
state) can be accurately represented in a truncated basis of Fock states, on a
wide time scale. At the same time, there can be arbitrarily large number of
observable quanta, especially if the open system is under driving. However, by
employing a Monte Carlo sampling of the measurement outcomes of the bath, we
can simulate the dynamics of the observable quantum field. In this work we
consider the measurement with respect to the coherent states, which yields the
Husimi function as the positive (quasi)probability distribution of the
outcomes. The evolution of dressed state which corresponds to a particular
fixed outcome is called the dressed qauntum trajectory. Therefore, the Monte
Carlo sampling of these trajectories yields a stochastic simulation method with
promising convergence properties on wide time scales.
