Fig. 1: Different descriptions of open quantum systems.

a A quantum system (blue disk) is interacting with an environment made of a continuum of non-interacting bosonic modes of angular frequencies ω. The strength of the interaction between the system and a given mode is encoded in the bath spectral density (SD) J(ω) (shown on the right). Markovian baths are described by a flat (i.e. constant) SD. A non-flat, i.e. structured, SD generally induces a non-Markovian dynamics. b Collision models construct non-interacting bosonic temporal-modes on a coarse-grained timescale that experience a finite number of interactions (collisions) with the system before being discarded (refreshed). c The chain mapping technique maps the bosonic environment into a non-uniform semi-infinite chain of interacting bosonic modes such that the system only couples to the first mode of the chain. d Chain mapping can be reformulated to make the modes non-interacting and coupling sequentially to the system for a finite amount of time. This reformulation is equivalent to collision models.