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Rosa edited untitled.tex
about 8 years ago
Commit id: 878e2eca80c4256f20fb397996cf170a6253e902
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index d218564..610083e 100644
--- a/untitled.tex
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&&N(\omega)=(e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi} V_{\beta k} V^*_{\gamma q}
[G_{\beta\nu}^r(\omega+\epsilon) V_{\nu q} g^{>}_{q}(\omega+\epsilon)+ G_{\beta\nu}^>(\omega+\epsilon) V_{\nu q} g^{a}_{q}(\omega+\epsilon)]
\\ \nonumber
&&[G_{\gamma\mu}^r(\omega) &&[G_{\gamma\mu}^r(\epsilon) V^*_{\mu k}
g^{<,h}_{k}(\omega)+ G_{\gamma\mu}^<(\omega) g^{<,h}_{k}(\epsilon)+ G_{\gamma\mu}^<(\epsilon) V^*_{\mu k}
g^{a,h}_{k}(\omega)] g^{a,h}_{k}(\epsilon)]
\end{eqnarray}
\begin{eqnarray}
N(\omega)&=&(e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi}
[G_{\beta\nu}^r(\omega+\epsilon) V_{\nu q} g^{>}_{q}(\omega+\epsilon) V^*_{\gamma q}
G_{\gamma\mu}^r(\omega) G_{\gamma\mu}^r(\epslion) V^*_{\mu k}
g^{<,h}_{k}(\omega) g^{<,h}_{k}(\epsilon) V_{\beta k}]
\\ \nonumber
&&[G_{\beta\nu}^r(\omega+\epsilon) V_{\nu q} g^{>}_{q}(\omega+\epsilon) V^*_{\gamma q}
G_{\gamma\mu}^<(\omega) G_{\gamma\mu}^<(\epsilon) V^*_{\mu k}
g^{a,h}_{k}(\omega) g^{a,h}_{k}(\epsilon) V_{\beta k}]
\\ \nonumber
&&[G_{\beta\nu}^>(\omega+\epsilon) V_{\nu q} g^{a}_{q}(\omega+\epsilon) V^*_{\gamma q}
G_{\gamma\mu}^r(\omega) G_{\gamma\mu}^r(\epsilon) V^*_{\mu k}
g^{<,h}_{k}(\omega) g^{<,h}_{k}(\epsilon) V_{\beta k}]
\\ \nonumber
&&[G_{\beta\nu}^>(\omega+\epsilon) V_{\nu q} g^{a}_{q}(\omega+\epsilon) V^*_{\gamma q}
G_{\gamma\mu}^<(\omega) G_{\gamma\mu}^<(\epsilon) V^*_{\mu k}
g^{a,h}_{k}(\omega) g^{a,h}_{k}(\epsilon) V_{\beta k}]
\end{eqnarray}
Inserting the expressions for the self-energies we get
\begin{eqnarray}
N(\omega)&=&(e^2/h)\sum_{k\beta,q\gamma, \nu\mu} \int \frac{d\epsilon}{2\pi}
[G_{\beta\nu}^r(\omega+\epsilon) \Sigma_{0,\nu\gamma}^>(\omega+\epsilon)
G_{\gamma\mu}^r(\omega) \Sigma_{0,\mu\beta}^{<,h}(\omega+\epsilon)] G_{\gamma\mu}^r(\epsilon) \Sigma_{0,\mu\beta}^{<,h}(\epsilon)]
\\ \nonumber
&&[G_{\beta\nu}^r(\omega+\epsilon) \Sigma_{0,\nu\gamma}^>(\omega+\epsilon)
G_{\gamma\mu}^<(\omega) \Sigma_{0,\mu\beta}^{a,h}(\omega+\epsilon)] G_{\gamma\mu}^<(\epsilon) \Sigma_{0,\mu\beta}^{a,h}(\epsilon)]
\\ \nonumber
&&[G_{\beta\nu}^>(\omega+\epsilon) \Sigma_{0,\nu\gamma}^a(\omega+\epsilon)
G_{\gamma\mu}^r(\omega)\Sigma_{0,\mu\beta}^{<,h}(\omega+\epsilon)] G_{\gamma\mu}^r(\epsilon)\Sigma_{0,\mu\beta}^{<,h}(\epsilon)]
\\ \nonumber
&&[G_{\beta\nu}^>(\omega+\epsilon) \Sigma_{0,\nu\gamma}^a(\omega+\epsilon)
G_{\gamma\mu}^<(\omega) \Sigma_{0,\mu\beta}^{a,h}(\omega)] G_{\gamma\mu}^<(\epsilon) \Sigma_{0,\mu\beta}^{a,h}(\epsilon)]
\end{eqnarray}
\begin{eqnarray}