Abstract
We explore the dynamics of $N$ coupled atoms to a generic bosonic reservoir
under specific system symmetries. In the regime of multiple atoms coupled to a
single reservoir with identical couplings, we identify remarkable effects,
notably that the initial configuration of the atomic excited state amplitudes
strongly impacts the dynamics of the system and can even fully sever the system
from its environment. Additionally, we find that steady state amplitudes of the
excited states become independent of the choice of the reservoir. The framework
introduced is applied to a structured photonic reservoir associated with a
photonic crystal, where we show it reproduces previous theoretical and
experimental results and it predicts superradiant behaviour within the
single-excitation regime.