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&V_{\beta k}^* V_{\gamma q}[g^{r,h}_{k}(\epsilon) V_{\alpha k} G_{\alpha\gamma}^>(\epsilon)+g^{>,h}_{k}(\epsilon) V_{\alpha k} G_{\alpha\gamma}^a(\epsilon)] [ V_{\gamma q} g^{r}_{q}(\omega+\epsilon) V^*_{\alpha q} G_{\alpha\beta}^<(\omega+\epsilon)+ V_{\gamma q} g^{<}_{q}(\epsilon) V^*_{\alpha q} G_{\alpha\beta}^a(\omega+\epsilon) ]  \end{align*}  Then we have  \begin{align*}  &Q^>(\omega) \begin{equation}  Q^>(\omega)  = \frac{ e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha} \int \frac{d\epsilon}{2\pi}[\Sigma_{0,\beta\alpha}^r (\epsilon)G_{\alpha\gamma}^>(\epsilon)+ \Sigma_{0,\beta\alpha}^> (\epsilon) G_{\alpha\gamma}^a(\epsilon)] \\  &[\Sigma^r_{0,\gamma [\Sigma^r_{0,\gamma  \alpha}(\omega+\epsilon) G_{\alpha\beta}^<(\omega+\epsilon)+ \Sigma^<_{0,\gamma \alpha}(\omega+\epsilon)G_{\alpha\beta}^a(\omega+\epsilon)] \end{align*} \end{equation}  We can split $Q^>(\omega)$ in four contributions  \begin{align*}  Q^{>,1}(\omega) &Q^{>,1}(\omega)  = \frac{ 4e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\mu\nu\tau,\delta\lambda} \int \frac{d\epsilon}{2\pi}[-i\Gamma_{\beta\alpha}]G_{\alpha\delta}^r(\epsilon)\Gamma_{\delta\lambda} G_{\lambda\gamma}^a(\epsilon) [-i\Gamma_{\gamma\tau}]G_{\tau\mu}^r(\omega+\epsilon)\Gamma_{\mu\nu} G_{\nu\beta}^a(\omega+\epsilon)  // G_{\nu\beta}^a(\omega+\epsilon)//  &((1-f_h(\epsilon)+(1-f_e(\epsilon)))(f_e(\omega+\epsilon)+f_h(\omega+\epsilon))  \end{align*} \end{align}  \begin{eqnarray}  Q^{>,2}(\omega) = \frac{ 4e^2}{\hbar^2}\sum_{k\beta,q\gamma,\alpha\mu\nu\tau} \int \frac{d\epsilon}{2\pi}[-i\Gamma_{\beta\alpha}]G_{\alpha\gamma}^a(\epsilon) [-i\Gamma_{\gamma\tau}]G_{\tau\mu}^r(\omega+\epsilon)\Gamma_{\mu\nu} G_{\nu\beta}^a(\omega+\epsilon) (1-f_h(\epsilon))(f_e(\omega+\epsilon)+f_h(\omega+\epsilon))