content_image/396725.jpg content_image/396727.jpg content_image/396729.jpg content_image/396726.jpg content_image/396728.jpg
<img src='content_image/396725.jpg'>

<img src='content_image/396727.jpg'>

and 

where we subtract the Fermi energy and the self-energy from their values in the electron-hole symmetric case n$_{f}$ = 1 / 2 , n$_{c}$ = 1 / 2. Explicit formulas are more involved and we do not present them here. Second, as discussed in Ref. 22, a nontrivial solution at zero temperature ex- ists only for 1 / 2 < n < 3 / 2. Outside this region the f -electron energy level is either empty ( n ≤ 1 / 2) or fully filled ( n ≥ 3 / 2). We plotted the Drude conductivity and DOS in Fig. 6 for a total filling n = 0 . 7. The density of states at the Fermi energy is almost constant within the interval 0 ≤ U ≤ 0 . 82, within which the extended electrons scatter on f -electrons. The extended electrons go over to a Fermi gas in both limiting values of inter- 

<img src='content_image/396729.jpg'>

<img src='content_image/396726.jpg'>

<img src='content_image/396728.jpg'>

action, hence the Drude conductivity diverges at both ends. The asymptotics is, however, different at the two ends. The asymmetry between the two limiting interac- tion strengths is demonstrated in Fig. 7, where we plot- ted the vertex correction to the Drude conductivity. It is two orders smaller than the mean-field one. This is clearly seen from their ratio plotted in Fig. 8. The ratio is no longer a monotonically increasing function as in the electron-hole symmetric case, but reaches maximum at U$_{m}$ ≈ 0 . 48. 

We studied effects of elastic scatterings of mobile elec- trons on either thermally equilibrated or frozen, ran- 

## VII. CONCLUSIONS 

