Composite quantum collision models

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.