Time-resolved Dyson equations in the context of time-dependent density-functional theory: Extension to solid systems

It is shown that under certain conditions an instantaneous resolvent $G\left(z;t\right)$ of a time-dependent Kohn-Sham or Kohn-Sham-Dirac operator $\mathcal{H}\left(t\right)$ can be defined from which the particle and the magnetization density can be evaluated directly using contour integrations. The corresponding Green’s function can be evaluated within a multiple-scattering scheme by solving at each given time $t$ coupled radial differential equations for the single-site problem. This scheme is in particular intriguing since within the adiabatic time-dependent density functional the configurational part of a time-dependent perturbation can be viewed as a contribution to an effective (full) potential. First applications are shown for an Fe atom excited by a femtosecond laser pulse.

Figure 1

(Color online) Variation in $\Delta E_B$ with respect to $W_0$ for selected $3d$ and $4p$ states of an Fe atom. The labeling is according to the angular momentum component of the given state that mostly contributes.

Figure 2

(Color online) Electric field in units of the interaction strength $W_0$ for a double-exponential laser pulse of intensity $I=6\text{mJ}/{\text{cm}}^2$.

Figure 3

(Color online) Calculated first-order transition probabilities [solid line: Eq. (49), dotted line: Eq. (46)] for selected transitions in an Fe atom due to a double-exponential laser pulse with $I=6\text{mJ}/{\text{cm}}^2$, ${\omega }_0=6.66{\text{fs}}^{-1}$, and $T_e=15\text{fs}$.

Figure 4

(Color online) Variation in the calculated transition probabilities with respect to the characteristics of a double-exponential laser pulse [see Eqs. (29, 45)] for a transition $3d_{5/2}-4p_{3/2}$ $\left(\mu =-1/2\right)$ in an Fe atom. The upper panel refers to ${\omega }_0=6.66{\text{fs}}^{-1}$, the lower one to $T_e=15\text{fs}$. In all cases the intensity of the laser pulse was fixed to $I=6\text{mJ}/{\text{cm}}^2$.