Relaxation in Time-Dependent Current-Density-Functional Theory

We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.

Figure 1

(a) Plot of the dipole moment $d(t)$ for the electrons in the quantum well as described in the text. (b) Plot of the Kohn-Sham energy $E(t)-E_0$. (c) Plot of $\Delta S(t)/\sqrt{2\gamma (E_i-E_0)}$ as given by Eqs. (12, 16). A fit of $E(t)$ using the data in (b) gives $\Gamma =0.0034\mathrm{a}.\mathrm{u}.$

Figure 2

The motion in the $z$ direction is coupled through the Coulomb interaction to a 2DEG in the $x\mathrm{\text{−}}y$ plane. The energy is lost to the motion in the $z$ direction at a rate given by $dE/dt$.