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53 lines
1.1 KiB
ReStructuredText
53 lines
1.1 KiB
ReStructuredText
.. index:: Transport
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.. _Transport:
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Transport calculations
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======================
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.. index:: Theory
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Formalism
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---------
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The optical conductivity and the Seebeck coefficient in the direction :math:`\alpha\beta` are defined as
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.. math::
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\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}}
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in which the kinetic coefficients :math:`A_{n,\alpha\beta}` are given by
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.. math::
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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)}
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with the transport distribution
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.. math::
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\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)
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.. index:: Prerequisite
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Prerequisites
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-------------
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.. note::
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Coming soon!
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.. index:: Using the transport code.
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Using the transport code
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------------------------
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.. note::
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Coming soon!
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.. index:: References
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References
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----------
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