  We consider the problem of electron transport along a one-dimensional
disordered multiple-scattering conductor, and study the electron density for
all the electronic levels. A model is proposed for the reduced density matrix
of the system placed between two reservoirs at different chemical potentials,
and the statistical-mechanical expectation value of the electron density is
evaluated. An ensemble average is computed over disordered configurations. We
compare its predictions with computer simulations. We find that the
contribution of low-lying levels is very different from that of the high-lying
ones studied in the past. Going down in energy, the wave function penetrates
ever less inside the sample. For high-lying levels, this is interpreted in
terms of localization from disorder. For low-lying levels, this interpretation
gradually gives way to an understanding in terms of the increasing reflection
produced by each scatterer, which is seen by the electron as a higher and
higher -- and hence impenetrable -- potential barrier. Indeed, the
local-density-of-states, LDOS, is gradually depleted in the interior of the
system, since the wave function is ever smaller inside. The problem studied
here is also of interest in electromagnetic, thermal, and acoustic transport in
disordered systems.
