  We present a comprehensive study of exciton wave packet evolution in
disordered lossless polaritonic wires. Our simulations reveal signatures of
ballistic, diffusive, and subdiffusive exciton dynamics under strong
light-matter coupling and identify the typical timescales associated with the
transitions between these qualitatively distinct transport phenomena. We
determine optimal truncations of the molecular subsystem and radiation field
required for generating reliable time-dependent data from computational
simulations at affordable cost. The time evolution of the photonic part of the
wave function reveals that many cavity modes contribute to the dynamics in a
non-trivial fashion. Hence, a sizable number of photon modes is needed to
describe exciton propagation with reasonable accuracy. We find and discuss an
intriguingly common lack of dominance of the photon mode on resonance with the
molecular system both in the presence and absence of disorder. We discuss the
implications of our investigations to the development of theoretical models and
analysis of experiments where coherent intermolecular energy transport and
static disorder play an important role.
