Composite quantum collision models (1705.03215v1)

Abstract: A collision model (CM) is a framework to describe open quantum dynamics. In its {\it memoryless} version, it models the reservoir $\mathcal R$ as consisting of a large collection of elementary ancillas: the dynamics of the open system $\mathcal{S}$ results from successive "collisions" of $\mathcal{S}$ with the ancillas of $\mathcal R$. Here, we present a general formulation of memoryless {\it composite} CMs, where $\mathcal S$ is partitioned into the very open system under study $S$ coupled to one or more auxiliary systems ${S_i}$. Their composite dynamics occurs through internal $S$-${S_i}$ collisions interspersed with external ones involving ${S_i}$ and the reservoir $\mathcal R$. We show that important known instances of quantum {\it non-Markovian} dynamics of $S$ -- such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise -- can be mapped on to such {\it memoryless} composite CMs.