Thermal Conductivity of Amorphous Silicon

Calculating the Thermal Conductivity of Amorphous Silicon with a Machine-Learning Force Field

Yufeng Huang et al. Phys. Rev. B 99, 064103 (2019)

Training-Set Accuracy

Test-Set Accuracy

Green-Kubo Formula

$$\kappa_{\mu\nu}(t)=\frac{1}{k_B T^2 V} \int_{0}^{t} dt' \langle J_\mu(0) J_\nu(t') \rangle$$ $$\mathbf{J} = \sum_{i} \mathbf{v}_i E_i + \sum_{i} \mathbf{r}_i \frac{d}{dt} E_i$$ $$= \sum_{i} \mathbf{v}_i (K_i + U_i) + \sum_{i} \mathbf{W}_i \cdot \mathbf{v}_i$$

Thermal Conductivity