Adiabatic Approximation in Nonperturbative Time-Dependent Density-Functional Theory

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.

Figure 1

Density, total KS potential, and correlation potential (from top to bottom) at the 3 times $t=0$, 21.5, 43.0 a.u. (from left to right) during the interaction of the two-electron atom with a dc electric field. Solid curves: exact time-dependent $v_s^{\mathrm{ex}}$ and $v_c^{\mathrm{ex}}$; dashed curves: adiabatically exact $v_s^{\mathrm{adia},\mathrm{ex}}$ and $v_c^{\mathrm{adia},\mathrm{ex}}$ (Hartree units). Note the different scales in the plots and that $v_c^{\mathrm{ex}}$ and $v_c^{\mathrm{adia},\mathrm{ex}}$ are very close, with deviations at the boundaries being a numerical consequence of low density; see text.

Figure 2

Same as Fig. 1 but for the two-electron atom during high-frequency excitation according to (8) at $t=\frac{1}{2}T$, $t=T=2\pi /\omega$ and $t=\frac{3}{2}T$ (from left to right). The initial situation at $t=0$ is the same as in Fig. 1.

Figure 3

Total ionization during the interaction of the two-electron atom with a laser pulse of maximum intensity $I_1=4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ (lower two curves) and $I_2=7\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ (upper two curves). Solid curves: exact TDSE calculation; dashed curves: adiabatically exact TDKS scheme. The inset shows a magnification of the first part of the curve.