Fig. 8: Vibrational DOS, specific heat, and diffusivity of vitreous silica.

a Red and green are the vDOS for the 192(D)⁶⁵ model (192-atom model generated from first-principles DFT simulations), obtained evaluating the frequencies of such model either from first principles or from the GAP potential, and using a 3 × 3 × 3 q mesh. The dashed blue line and gray area are the vDOS of the GAP-generated⁶⁰ 192- and 5184-atom models, computed using GAP as in Fig. 4 (i.e., relying on a 3 × 3 × 3 q mesh in the former case, and at q = 0 only in the latter case). b Solid lines are the quantum harmonic specific heat as a function of frequency and temperature from Eq. (2). The dashed line are the classical specific heat. c Harmonic Allen-Feldman thermal diffusivity computed from Eq. (8) using Γ(q)_s = 0 ∀ q, s and with the models discusses in a (same parameters and color code); the inset shows that in v-SiO₂ (5184(G) model) the AF diffusivity is very similar to the anharmonic diffusivity (full Eq. (8)).