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An approach, called discretized environment method, is introduced to treatexactly non-Markovian effects in open quantum systems. In this approach, acomplex environment described by a spectral function is mapped into a finiteset of discretized states with an appropriate coupling to the system ofinterest. The finite set of system plus environment degrees of freedom are thenexplicitly followed in time leading to a quasi-exact description. The presentapproach is anticipated to be particularly accurate in the low temperature andstrongly non-Markovian regime. The discretized environment method is validatedon a two-level system (qubit) coupled to a bosonic or fermionic heat bath. Aperfect agreement with the quantum Langevin approach is found. Furtherillustrations are made on a three-level system (qutrit) coupled to a bosonicheat-bath. Emerging processes due to strong memory effects are discussed.

Exact description of non-Markovian effect in open quantum system: the discretized environment method