  The process by which a nuclear projectile is decelerated by the electrons of
the condensed matter it traverses is currently being studied by following the
explicit dynamics of projectile and electrons from first principles in a
simulation box with a sample of the host matter in periodic boundary
conditions. The approach has been quite successful for diverse systems even in
the strong-coupling regime of maximal dissipation. This technique is here
revisited for periodic solids in the light of the Floquet theory of stopping, a
time-periodic scattering framework characterizing the stationary
dynamicalsolutions for a constant velocity projectile in an infinite solid. The
effect of proton projectiles in diamond is studied under that light, using
time-dependent density-functional theory in real time. The Floquet quasi-energy
conserving stationary scattering regime, characterized by time-periodic
properties such as particle density and the time derivative of energy, is
obtained for a converged system size of one thousand atoms. The validity of the
customary calculation of electronic stopping power from the average slope of
the density-functional total energy is discussed. Quasi-energy conservation, as
well as the implied fundamental approximations, are critically reviewed.
