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