  The exact exchange-correlation (XC) potential in time-dependent
density-functional theory (TDDFT) is known to develop steps and discontinuities
upon change of the particle number in spatially confined regions or isolated
subsystems. We demonstrate that the self-interaction corrected adiabatic
local-density approximation for the XC potential has this property, using the
example of electron loss of a model quantum well system. We then study the
influence of the XC potential discontinuity in a real-time simulation of a
dissociation process of an asymmetric double quantum well system, and show that
it dramatically affects the population of the resulting isolated single quantum
wells. This indicates the importance of a proper account of the discontinuities
in TDDFT descriptions of ionization, dissociation or charge transfer processes.
