  We study optical spectra of finite electronic quantum systems at frequencies
smaller than the plasma frequency using a quasi-classical approach. This
approach includes collective effects and enables us to analyze how the nature
of the (single-particle) electron dynamics influences the optical spectra in
finite electronic quantum systems. We derive an analytical expression for the
low-frequency absorption coefficient of electro-magnetic radiation in a finite
quantum system with ballistic electron dynamics and specular reflection at the
boundaries: a two-dimensional electron gas confined to a strip of width a (the
approach can be applied to systems of any shape and electron dynamics --
diffusive or ballistic, regular or irregular motion). By comparing with results
of numerical computations using the random-phase approximation we show that our
analytical approach provides a qualitative and quantitative understanding of
the optical spectrum.
