LCPQ/dft_tools
3
0
Fork 0
mirror of https://github.com/triqs/dft_tools synced 2025-01-02 17:45:47 +01:00
Code Issues Releases Wiki Activity

bugfixes in the transport doc

Browse Source
This commit is contained in:
aichhorn 2015-10-02 13:47:46 +02:00
parent 31bf191cf8
commit ec414f40ff
1 changed files with 3 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
doc/guide/transport.rst
View File

@ -15,13 +15,13 @@ in which the kinetic coefficients :math:`A_{n,\alpha\beta}` are given by
.. math:: .. 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)}. 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,\omega\right)}.
Here :math:`N_{sp}` is the spin factor and :math:`f(\omega)` is the Fermi function. The transport distribution :math:`\Gamma_{\alpha\beta}\left(\omega\right)` is defined as Here :math:`N_{sp}` is the spin factor and :math:`f(\omega)` is the Fermi function. The transport distribution :math:`\Gamma_{\alpha\beta}\left(\omega_1,\omega_2\right)` is defined as
.. math:: .. math::
\Gamma_{\alpha\beta}\left(\omega\right) = \frac{1}{V} \sum_k Tr\left(v_{k,\alpha}A_{k}(\omega)v_{k,\beta}A_{k}\left(\omega\right)\right), \Gamma_{\alpha\beta}\left(\omega_1,\omega_2\right) = \frac{1}{V} \sum_k Tr\left(v_{k,\alpha}A_{k}(\omega_1)v_{k,\beta}A_{k}\left(\omega_2\right)\right),
where :math:`V` is the unit cell volume. In multi-band systems the velocities :math:`v_{k}` and the spectral function :math:`A(k,\omega)` are matrices in the band indices :math:`i` and :math:`j`. where :math:`V` is the unit cell volume. In multi-band systems the velocities :math:`v_{k}` and the spectral function :math:`A(k,\omega)` are matrices in the band indices :math:`i` and :math:`j`.
The frequency depended optical conductivity is given by The frequency depended optical conductivity is given by