  An approach, called discretized environment method, is introduced to treat
exactly non-Markovian effects in open quantum systems. In this approach, a
complex environment described by a spectral function is mapped into a finite
set of discretized states with an appropriate coupling to the system of
interest. The finite set of system plus environment degrees of freedom are then
explicitly followed in time leading to a quasi-exact description. The present
approach is anticipated to be particularly accurate in the low temperature and
strongly non-Markovian regime. The discretized environment method is validated
on a two-level system (qubit) coupled to a bosonic or fermionic heat bath. A
perfect agreement with the quantum Langevin approach is found. Further
illustrations are made on a three-level system (qutrit) coupled to a bosonic
heat-bath. Emerging processes due to strong memory effects are discussed.
