diff --git a/doc/Transport.rst b/doc/Transport.rst new file mode 100644 index 00000000..c86af09e --- /dev/null +++ b/doc/Transport.rst @@ -0,0 +1,52 @@ +.. index:: Transport + +.. _Transport: + +Transport calculations +====================== + +.. index:: Theory + +Formalism +--------- +The optical conductivity and the Seebeck coefficient in the direction :math:`\alpha\beta` are defined as + +.. math:: + + \sigma_{\alpha\beta} = \beta e^{2} A_{0,\alpha\beta} \ \ \ \text{and} \ \ \ S_{\alpha\beta} = -\frac{k_B}{|e|}\frac{A_{1,\alpha\beta}}{A_{0,\alpha\beta}} + +in which the kinetic coefficients :math:`A_{n,\alpha\beta}` are given by + +.. math:: + + A_{n,\alpha\beta} = N_{sp} \pi \hbar \int{d\omega \left(\beta\omega\right)^n f\left(\omega\right)f\left(-\omega\right)\Gamma_{\alpha\beta}\left(\omega\right)} + +with the transport distribution + +.. math:: + + \Gamma_{\alpha\beta}\left(\omega\right) = \frac{1}{V} \sum_k Tr\left(v_{k,\alpha}A_{k}\left(\omega\right)v_{k,\beta}A_{k}\left(\omega\right)\right) + +.. index:: Prerequisite + +Prerequisites +------------- + +.. note:: + Coming soon! + + +.. index:: Using the transport code. + +Using the transport code +------------------------ + +.. note:: + Coming soon! + + +.. index:: References + +References +---------- +