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Split conductivity_and_seebeck, cleaning up, doc

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Manuel Zingl 2014-12-18 16:49:35 +01:00 committed by Priyanka Seth
parent f24913b8a7
commit fd7ab682a4

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.. 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
----------