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The standard theoretical descriptions of the dynamics of open quantum systemsrely on the assumption that the correlations with the environment can beneglected at some reference (initial) time. While being reasonable in specificinstances, such as when the coupling between the system and the environment isweak or when the interaction starts at a distinguished time, the use ofinitially uncorrelated states is questionable if one wants to deal with generalmodels, taking into account the mutual influence that the open-system andenvironmental evolutions perform on each other. Here, we introduce aperturbative method that can be applied to any microscopic modeling of thesystem-environment interaction, including fully general initial correlations.Extending the standard technique based on projection operators that single outthe relevant part of the global dynamics, we define a family of projectionsadapted to a convenient decomposition of the initial state, which involves aconvex mixture of product operators with proper environmental states. Thisleads us to characterize the open-system dynamics via an uncoupled system ofdifferential equations, which are homogeneous and whose number is limited bythe dimensionality of the open system, for any kind of initial correlations.Our method is further illustrated by means of two cases study, for which itreproduces the expected dynamical behavior in the long-time regime moreconsistently than the standard projection technique.

Adapted projection operator technique for the treatment of initial correlations