  We investigate the collective plasmonic modes in a chain of metallic
nanoparticles that are coupled by near-field interactions. The size- and
momentum-dependent nonradiative Landau damping and radiative decay rates are
calculated analytically within an open quantum system approach. These decay
rates determine the excitation propagation along the chain. In particular, the
behavior of the radiative decay rate as a function of the plasmon wavelength
leads to a transition from an exponential decay of the collective excitation
for short distances to an algebraic decay for large distances. Importantly, we
show that the exponential decay is of a purely nonradiative origin. Our
transparent model enables us to provide analytical expressions for the
polarization-dependent plasmon excitation profile along the chain and for the
associated propagation length. Our theoretical analysis constitutes an
important step in the quest for the optimal conditions for plasmonic
propagation in nanoparticle chains.
