Time-dependent Kohn-Sham theory with memory

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic local density approximation can be described in terms of viscoelastic stresses in the electron liquid. In the time domain, this leads to a velocity-dependent xc vector potential with a memory containing short- and long-range components. The resulting time-dependent Kohn-Sham formalism describes the dynamics of electronic systems including decoherence and relaxation. For the example of collective charge-density oscillations in a quantum well, we illustrate the xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations.