  We investigate theoretically the formation of collective excitations in
atomic scale quasi-one dimensional metallic nanostructures. The response of the
system is calculated within the linear response theory and random phase
approximation. For uniform nanostructures a transition from quantum single
particle excitations to classical plasmon scaling is observed, depending on the
system length and electron density. We find crucial differences in the scaling
behavior for quasi-one dimensional and three-dimensional nanostructures. The
presence of an additional modulating on-site potential is shown to localize
electrons, leading to the response function that is highly sensitive to the
number of electrons at low fillings.
