  This paper describes experiments utilizing a unique property of
electron-glasses to gain information on the fundamental nature of the
interacting Anderson-localized phase. The methodology is based on measuring the
energy absorbed by the electronic system from alternating electromagnetic
fields as function of their frequency. Experiments on three-dimensional (3D)
amorphous indium-oxide films suggest that, in the strongly localized regime,
the energy spectrum is discrete and inelastic electron-electron events are
strongly suppressed. These results imply that, at low temperatures, electron
thermalization and finite conductivity depend on coupling to the phonon bath.
The situation is different for samples nearing the metal-insulator transition;
in insulating samples that are close to the mobility-edge, energy absorption
persists to much higher frequencies. Comparing these results with previously
studied 2D samples [Ovadyahu, Phys. Rev. Lett., 108, 156602 (2012)]
demonstrates that the mean-level spacing (on a single-particle basis) is not
the only relevant scale in this problem. The possibility of de-localization by
many-body effects and the relevance of a nearby mobility-edge (which may be a
many-body edge) are discussed.
