  We derive a non-Markovian master equation for the evolution of a class of
open quantum systems consisting of quadratic fermionic models coupled to
wide-band reservoirs. This is done by providing an explicit correspondence
between master equations and non-equilibrium Green's functions approaches. Our
findings permit to study non-Markovian regimes characterized by negative
decoherence rates. We study the real-time dynamics and the steady-state
solution of two illustrative models: a tight-binding and an XY-spin chains. The
rich set of phases encountered for the non-equilibrium XY model extends
previous studies to the non-Markovian regime.
