B. Useful Identities

Several identities from tensor and vector analysis used throughout the derivation of transport models in this work are listed below.

$$\ensuremath{\mathitbf{a}} \ensuremath{\cdot}\ensuremath{\ensurema... ...\ensuremath{\mathitbf{a}} \ensuremath{\otimes}\ensuremath{\mathitbf{c}} \right)$$ (B.1)

$$\ensuremath{\mathitbf{a}} \ensuremath{\cdot}\ensuremath{\ensurema... ...emath{\mathitbf{\nabla}}}\ensuremath{\otimes}}\ensuremath{\mathitbf{a}} \right)$$ (B.2)

$$\ensuremath{\ensuremath{\ensuremath{\mathitbf{\nabla}}}\ensuremat... ...emath{\mathitbf{\nabla}}}\ensuremath{\otimes}}\ensuremath{\mathitbf{a}} \right)$$ (B.3)

$$\ensuremath{\frac{1}{\hbar} \ensuremath{\ensuremath{\mathitbf{\na... ...times}\ensuremath{\mathitbf{p}} \right) \frac{1}{p} \ensuremath{\partial_{p} h}$$ (B.4)

$$\ensuremath{\mathitbf{a}} \left( \ensuremath{\mathitbf{b}} \ensur... ...\ensuremath{\mathitbf{b}} \ensuremath{\otimes}\ensuremath{\mathitbf{a}} \right)$$ (B.5)

$$\ensuremath{\frac{1}{\hbar} \ensuremath{\ensuremath{\mathitbf{\na... ...suremath{\frac{1}{\hbar} \ensuremath{\ensuremath{\mathitbf{\nabla_{\!k}}}}}h(p)$$ (B.6)

$$\ensuremath{\mathitbf{a}} \ensuremath{\ensuremath{\ensuremath{\ma... ...{\mathitbf{\nabla_{\!r}}}}\ensuremath{\cdot}}\ensuremath{\mathitbf{a}} \equiv 0$$ (B.7)

M. Wagner: Simulation of Thermoelectric Devices