The nanofabrication technology has taught us that an m-dimensional confining potential imposed upon an n-dimensional electron gas paves the way to a quasi-(n-m)-dimensional electron gas, with m ? n and 1 ? n, m ? 3. This is the road to the (semiconducting) quasi-n dimensional electron gas systems we have been happily traversing on now for almost two decades. Achieving quasi-one dimensional electron gas (Q-1DEG) [or quantum wire(s) for more practical purposes] led us to some mixed moments in this journey: while the reduced phase space for the scattering led us believe in the route to the faster electron devices, the proximity to the 1D systems left us in the dilemma of describing it as a Fermi liquid or as a Luttinger liquid. No one had ever suspected the potential of the former, but it took quite a while for some to convince the others on the latter. A realistic Q-1DEG system at the low temperatures is best describable as a Fermi liquid rather than as a Luttinger liquid. In the language of condensed matter physics, a critical scrutiny of Q-1DEG systems has provided us with a host of exotic (electronic, optical, and transport) phenomena unseen in their higher- or lower-dimensional counterparts. This has motivated us to undertake a systematic investigation of the inelastic electron scattering (IES) and the inelastic light scattering (ILS) from the elementary electronic excitations in quantum wires. We begin with the Kubo's correlation functions to derive the generalized dielectric function, the inverse dielectric function, and the Dyson equation for the dynamic screened potential in the framework of Bohm-Pines’ random-phase approximation. These fundamental tools then lead us to develop methodically the theory of IES and ILS for the Q-1DEG systems. As an application of the general formal results, which know no bounds regarding the subband occupancy, we compute the density of states, the Fermi energy, the full excitation spectrum [comprised of intrasubband and intersubband single-particle as well as collective excitations], the loss functions for the IES and the Raman intensity for the ILS. We observe that it is the collective (plasmon) excitations that largely contribute to the predominant peaks in the energy-loss and the Raman spectra. The inductive reasoning is that the IES can be a potential alternative of the overused ILS for investigating collective excitations in quantum wires. We trust that this research work shall be useful to all – from novice to expert and from theorist to experimentalist – who believe in the power of traditional science.
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