  Recently, a large class of quantum non-Markovian piecewise dynamics for an
open quantum system obeying closed evolution equations has been introduced [B.
Vacchini, Phys. Rev. Lett. 117, 230401 (2016)]. These dynamics have been
defined in terms of a waiting-time distribution between quantum jumps, along
with quantum maps describing the effect of jumps and the system's evolution
between them. Here, we present a quantum collision model with memory, whose
reduced dynamics in the continuous-time limit reproduces the above class of
non-Markovian piecewise dynamics, thus providing an explicit microscopic
realization.
