  The chain mapping of structured environments is a most powerful tool for the
simulation of open quantum system dynamics. Once the environmental bosonic or
fermionic degrees of freedom are unitarily rearranged into a one dimensional
structure, the full power of Density Matrix Renormalization Group (DMRG) can be
exploited. Beside resulting in efficient and numerically exact simulations of
open quantum systems dynamics, chain mapping provides an unique perspective on
the environment: the interaction between the system and the environment creates
perturbations that travel along the one dimensional environment at a finite
speed, thus providing a natural notion of light-, or causal-, cone. In this
work we investigate the transport of excitations in a chain-mapped bosonic
environment. In particular, we explore the relation between the environmental
spectral density shape, parameters and temperature, and the dynamics of
excitations along the corresponding linear chains of quantum harmonic
oscillators. Our analysis unveils fundamental features of the environment
evolution, such as localization, percolation and the onset of stationary
currents.
