  Electron localization is the tendency of an electron in a many-body system to
exclude other electrons from its vicinity. Using a new natural measure of
localization based on the exact manyelectron wavefunction, we find that
localization can vary considerably between different ground-state systems, and
can also be strongly disrupted, as a function of time, when a system is driven
by an applied electric field. We use our new measure to assess the well-known
electron localization function (ELF), both in its approximate single-particle
form (often applied within density-functional theory) and its full
many-particle form. The full ELF always gives an excellent description of
localization, but the approximate ELF fails in time-dependent situations, even
when the exact Kohn-Sham orbitals are employed.
