A quantum non-Markovian collision model: incoherent swap case

We have recently presented a collision-model-based framework to tackle non-Markovian quantum dynamics (Ciccarello et al 2012 arXiv:1207.6554). As a distinctive feature, memory is introduced in a dynamical way by adding extra inter-ancillary collisions to a standard (memoryless) collision model. In this paper, 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.