Composite quantum collision models

A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R as consisting of a large collection of elementary ancillas: the dynamics of the open system S results from successive collisions of S with the ancillas of R. Here, we present a general formulation of memoryless composite CMs, where 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 R. We show that important known instances of quantum 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 memoryless composite CMs.