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In this paper we investigate non-Markovian evolution of a two-level system(qubit) in a bosonic bath under influence of an external classical fluctuatingenvironment. The interaction with the bath has the Lorentzian spectral density,and the fluctuating environment (stochastic field) is represented by a set ofOrnstein-Uhlenbeck processes. Each of the subenvironments of the compositeenvironment is able to induce non-Markovian dynamics of the two-level system.By means of the numerically exact method of hierarchical equations of motion,we study dependence of the steady states of the two-level system, the reduceddensity matrix evolution and the equilibrium emission spectrums on frequencycutoffs and coupling strengths of the subenvironments. Additionally weinvestigate the impact of the rotation-wave approximation (RWA) used for theinteraction with the bath on accuracy of the results.

Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time