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\Sigma^{r,e}_{\alpha\delta}(\epsilon) = -i\Gamma_{\alpha\delta}(\epsilon),\quad \Sigma^{a,e}_{\alpha\delta} = i\Gamma_{\alpha\delta}(\epsilon)  \end{equation}  Similar equations are hold for $\Sigma^{>,e }(\epsilon)= -2i [1-f_{e}(\epsilon)] \Gamma_{\alpha\delta}(\epsilon)$ and$\Sigma^{>,h}(\epsilon)= -2i [1-f_{h}(\epsilon)] \Gamma_{\alpha\delta}(-\epsilon)$. Then,  \begin{eqnarray}  &&P^{>,1}(\omega)= \begin{align*}  &P^{>,1}(\omega)=  \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) \Sigma^>_{0,\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon)\Sigma^{h,<}_{0,\alpha\delta}(\epsilon+\omega) \\ \nonumber && &  = -4 \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [ (1-f_{e}(\epsilon)) \Gamma_{\alpha\delta}(\epsilon) + (1-f_{h}(\epsilon)) \Gamma_{\alpha\delta}(-\epsilon)] G^a_{\delta \gamma}(\epsilon) f_{h}(\epsilon) \Gamma_{\alpha\delta}(-(\epsilon+\omega))] \end{eqnarray} \end{align*}  In the particle-hole case we take $\Gamma(\epsilon)=\Gamma(-\epsilon)$. Besides we consider the WBL and take $\Gamma$ as constants, then  \begin{eqnarray}  && \begin{align*}  &  P^{>,1}(\omega)= \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha} G^r_{\beta \alpha}(\epsilon) \Sigma^>_{0,\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon)\Sigma^{h,<}_{0,\alpha\delta}(\epsilon+\omega) \\ \nonumber  &=& \gamma}(\epsilon)\Sigma^{h,<}_{0,\alpha\delta}(\epsilon+\omega)=  \frac{4e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta} [G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta} G^a_{\delta \gamma}(\epsilon) \Gamma_{\alpha\delta} \\ \nonumber  && [(1-f_{e}(\epsilon))f_{h}(\epsilon+\omega)+(1-f_{h}(\epsilon)) &[(1-f_{e}(\epsilon))f_{h}(\epsilon+\omega)+(1-f_{h}(\epsilon))  f_{h}(\epsilon+\omega)] \end{eqnarray} \end{align*}  \begin{eqnarray}  && P^{>,2}(\omega) = \frac{4e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{\beta\gamma\alpha\delta\tau\theta} \\ \nonumber  && G^r_{\beta \alpha}(\epsilon) \Gamma_{\alpha\delta}(\epsilon) G^a_{\delta \gamma}(\epsilon) [-i\Gamma_{\gamma\tau}] G^{r}_{\tau\theta}(\omega+\epsilon) \Gamma_{\theta\beta}[(1-f_{e}(\epsilon))f_{h}(\epsilon+\omega)+(1-f_{h}(\epsilon)) f_{h}(\epsilon+\omega)]