Reply to “Comment on ‘Electron transport through correlated molecules computed using the time-independent Wigner function: Two critical tests’ ”

In their Comment, Greer et al. (i) put us in charge of a pretended wrong claim, which we never made in our paper of Phys. Rev. B 78, 115315 (2008), where we criticized a method (DG) proposed by two of them, (ii) incorrectly claim that the DG method can reproduce the conductance quantum $g_0$, but (iii) to deduce $g_0$ for a toy model, they carry out calculations within the standard Landauer method, which has nothing to do with the DG’s. We present results for their model obtained within the DG method, which demonstrate that the DG method fails as lamentably as in the examples we presented in our earlier work. We also analyze the physical reasons why the DG method fails.

Figure 1

(Color online) I-V characteristics obtained exactly from Eq. (1) for infinite electrodes with $k_F=12{\text{nm}}^{-1}$ (as in gold), and for two finite sizes $L$ (given in the legend).

Figure 2

(Color online) Equilibrium Wigner function computed: (a, b) using the GDF formulas, and (c) for a confined system for two sizes $L$ (given in the legend) and $k_F=p_F/\hslash =12{\text{nm}}^{-1}$.

Figure 3

(Color online) (a) Deviation from equilibrium of the Wigner function at the boundaries $\delta f\left(-L/4,p\right)=-\delta f\left(+L/4,-p\right)$ for the confined and periodic cases (superscripts $o$ and $p$, respectively) [see the main text and Eq. (8)]; (b, c) The very slow convergence of $\delta f\left(-L/4,p\right)$ by increasing all the exact multielectronic eigenstates up to high excitation energies $\Delta \epsilon =r{\epsilon }_F$ ($r$ is given in inset) substantially larger than the metallic electrode bandwidth $\left(\sim {\epsilon }_F\right)$. Because of rapid oscillations, only the range around the Fermi momentum $p_F$ is shown in (b).