Memory kernel and divisibility of Gaussian collisional models

Memory effects in the dynamics of open systems have been subject significant interest last decades. The methods involved quantifying this effect, however, are often difficult to compute and may lack analytical insight. With mind, we consider Gaussian collisional models, where non-Markovianity is introduced by means additional interactions between neighboring environmental units. By focusing on continuous-variable dynamics, able analytically study models arbitrary size. We show that can be cast terms a Markovian Embedding covariance matrix, which yields closed form expressions for memory kernel governs quantity seldom computed analytically. same also possible divisibility monotone, based complete positivity intermediate maps. analyze detail two types interactions, beam-splitter implementing partial SWAP two-mode squeezing, entangles ancillas and, at time, feeds excitations into system. analyzing these representative scenarios, our results help shed light intricate mechanisms behind quantum domain.