Time-dependent transition density matrix

► A time-dependent generalization of the transition density matrix (TDM) is proposed. ► The time-dependent TDM is approximately calculated using Kohn-Sham wave functions. ► Numerical examples on one-dimensional lattices illustrate how the TDM works. ► Rapid formation and spreading of electron-hole pairs is observed. ► Here, electron interaction effects are less important than quantum confinement.