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

Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale