  We have recently presented a collision-model-based framework to approach
non-Markovian quantum dynamics [Ciccarello F Palma G M and Giovannetti V 2013
Phys. Rev. A 87, 040103(R)]. As a distinctive feature, memory is introduced in
a dynamical way by adding extra inter-ancillary collisions to a standard
(memoryless) collision model. Here, we focus on the case where such intra-bath
collisions are described by incoherent partial swap operations. After briefly
reviewing the model, we show how to include temperature as an additional
parameter by relaxing the assumption that each bath ancilla is initially in a
pure state. We also calculate explicitly the dynamical map entailed by the
master equation in the paradigmatic instance of a Jaynes-Cummings
system-ancilla coupling.
