Fig. 4. Convergence of the anharmonic Wigner conductivity in finite-size v-SiO₂ models.

Top, bare WTE conductivity (Eqs. (1), (4)) from the 192-atom (blue), 1536-atom (green), or 5184-atom (orange) model, and evaluated at q = 0 (solid lines) or on a 3 × 3 × 3 q mesh to extrapolate to the bulk limit (dashed lines). The crystal-like divergence of the WTE conductivity computed using the q mesh is a finite-size effect, occurring at lower temperatures for larger models. For T > 250 K, in the 1536-atom and 5184-atom models the conductivities computed at q = 0 are indistinguishable from those computed using the q mesh; for the 192-atom model, instead, employing the q interpolation is crucial to obtain the correct bulk limit. Bottom, regularized WTE conductivity (rWTE) for the 192- (solid black) or 5184-atom (empty diamonds) model, both computed using a 3 × 3 × 3 q mesh. The rWTE smoothly connects the correct low- and high-temperature limits, i.e., the fully q-sampled AF conductivity (as in Fig. 1, the dashed-dotted red line is the 192-atom model, empty red circles are the 5184-atom model) and the bare WTE (dashed blue), respectively. Inset: the bare WTE conductivity computed at q = 0 for the 1536- and 5184-atom models are practically equal to the q-sampled rWTE conductivity of the 192-atom model; for the 1536- and 5184-atom models the bare WTE conductivity at q = 0 is practically equivalent to the rWTE conductivity computed on a 3 × 3 × 3 q mesh.