Non-Markovian effects in electronic and spin transport

We derive a non-Markovian master equation for the evolution of a class of open quantum systems consisting of quadratic fermionic systems coupled to wideband reservoirs. This is done by providing an explicit correspondence between master equations and nonequilibrium Green's function approaches. Our findings permit us to address non-Markovian regimes characterized by negative decoherence rates and to characterize the dynamics with respect to a recently proposed measurement of non-Markovianity. We study the real-time dynamics and the steady-state solution of two illustrative models: a tight-binding electronic model and XY spin chains. The rich set of nonequilibrium steady-state phases encountered extends previous results to the non-Markovian regime.