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Master equations are commonly used to describe time evolution of opensystems. We introduce a general method for calculating a Markovian solution ofthe Nakajima-Zwanzig generalized master equation. We do so for a time dependenttransport of interacting electrons through a complex nano scale system in aphoton cavity. The central system, described by 120 many-body states in a Fockspace, is weakly coupled to the external leads. The very diverse relaxationtimes of the open system, reflecting radiative or non-radiative transitions,require information about the time evolution through many orders of magnitude.In our approach, the generalized master equation is mapped from a many-bodyFock space of states to a Liouville space of transitions. We show that thisresults in a linear equation which is solved exactly through an eigenvalueanalysis, which supplies information on the steady state and the time evolutionof the system.

Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system