  We report on the theoretical investigation of the elementary electronic
excitations in a quantum wire made up of vertically stacked self-assembled
InAs/GaAs quantum dots. The length scales (of a few nanometers) involved in the
experimental setups prompt us to consider an infinitely periodic system of
two-dimensionally confined (InAs) quantum dot layers separated by GaAs spacers.
The the Bloch functions and the Hermite functions together characterize the
whole system. We then make use of the Bohm-Pines' (full) random-phase
approximation in order to derive a general nonlocal, dynamic dielectric
function. Thus developed theoretical framework is then specified to work within
a (lowest miniband and) two-subband model that enables us to scrutinize the
single-particle as well as collective responses of the system. We compute and
discuss the behavior of the eigenfunctions, band-widths, density of states,
Fermi energy, single-particle and collective excitations, and finally size up
the importance of studying the inverse dielectric function in relation with the
quantum transport phenomena. It is remarkable to notice how the variation in
the barrier- and well-widths can allow us to tailor the excitation spectrum in
the desired energy range. Given the advantage of the vertically stacked quantum
dots over the planar ones and the foreseen applications in the single-electron
devices and in the quantum computation, it is quite interesting and important
to explore the electronic, optical, and transport phenomena in such systems.
