Time-dependent current-density-functional theory taking into consideration the effect of energy dissipation

As a microscopic theory to express the electromagnetic response of the system to the external fields, we present the time-dependent current-density-functional theory (td-CDFT), taking into account the effect of the energy dissipation from the system. In order to express such an effect, the non-Hermitian term which corresponds to the lifetime of the higher-energy component of the many-electron state is added to the Hamiltonian of the system. Specifically, the occupation number of the Bloch states, the energies of which are higher than the Fermi energy, is chosen as a basic variable in addition to the electron density and paramagnetic current density. In order to confirm its validity, the present td-CDFT is applied to the two-level system. We successfully revisit the electric susceptibility of the Drude-Lorentz model via the present theory.