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\end{eqnarray}  We now compute separately the different parts of the previous expression for the ac noise  \begin{eqnarray}  P^{>,1}(\omega)= \frac{e^2}{\hbar^2}\int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} \frac{d\epsilon}{2\pi}\sum_{k,q,p\beta\gamma\alpha\delta}  G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^>_{p}(\epsilon)V_{ \delta p} + V_{\alpha p} g^{h,>}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon)[V_{\beta k} g_{q}^{h,<}(\omega+\epsilon)V^*_{\gamma q}\delta_{kq} (\Sigma_{0,\alpha\delta}^{>}+ \Sigma_{0,\alpha\delta}^{>,h}) G^a_{\delta \gamma}(\epsilon)\Sigma_{\gamma\beta}^{<,h}(\omega+\epsilon)\delta_{kq}  \end{eqnarray}  \begin{eqnarray}  &&P^{>,2}(\omega) P^{>,2}(\omega)  = \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} \sum_{k,q,p\beta\gamma\alpha\delta\tau\theta}  G^r_{\beta \alpha}(\epsilon) [V_{\alpha p}^* g^>_{p}(\epsilon)V_{\delta p} + V_{\alpha p} g^{h,>}_{p}(\epsilon) V_{\delta p}^*]G^a_{\delta (\Sigma_{0,\alpha\delta}^{>}+ \Sigma_{0,\alpha\delta}^{>,h}) G^a_{\delta  \gamma}(\epsilon)\\ \nonumber  && [V_{\gamma q}^* g_{q}^{h,r}(\omega+\epsilon) V_{\gamma q} G^{<}_{\gamma\beta}(\omega+\epsilon) V_{\beta k} g_{k}^{h,a}(\omega+\epsilon) V_{\beta k}^*]  \end{eqnarray}  \begin{eqnarray}  &&P^{>,3}(\omega)= \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \sum_{k,q,p\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^>_{p}(\epsilon)V_{ \delta p} P^{>,3}(\omega) =  \Sigma_{\gamma\tau}^{r,h}(\omega+\epsilon) G_{\tau\theta}^r(\omega+\epsilon)\Sigma_{\theta\beta}^{r,<}(\omega+\epsilon)  + V_{\alpha p} g^{h,>}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon) \\ \nonumber   && [V_{\gamma q}^* g_{k}^{h,r}(\omega+\epsilon) V^*_{\gamma q} G^{<}_{\gamma\beta}(\omega+\epsilon)V_{\gamma q} g_{q}^{h,a}(\omega+\epsilon) V^*_{\gamma q}] \Sigma_{\gamma\tau}^{r,h}(\omega+\epsilon) G_{\tau\theta}^<(\omega+\epsilon)\Sigma_{\theta\beta}^{a,<}(\omega+\epsilon)  \end{eqnarray}  \begin{eqnarray}  &&P^{>,4}(\omega)= \frac{e^2}{\hbar^2} \int_{-\infty}^\infty \frac{d\epsilon}{2\pi} \sum_{k,q,p\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon)[V^*_{\alpha p} g^>_{p}(\epsilon)V_{ \delta p } P^{>,4}(\omega) =\Sigma_{\gamma\tau}^{r,h}(\omega+\epsilon) G_{\tau\theta}^r(\omega+\epsilon)\Sigma_{\theta\beta}^{r,<}(\omega+\epsilon)  + V_{\alpha p} g^{h,>}_{p}(\epsilon) V^*_{\delta p}] G^a_{\delta \gamma}(\epsilon)\\ \nonumber   && [V_{\beta k} g_{k}^{h,<}(\omega+\epsilon) V_{\gamma k} G^{a}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{h,a}(\omega+\epsilon)V^*_{\gamma q}] \Sigma_{\gamma\tau}^{<,h}(\omega+\epsilon) G_{\tau\theta}^a(\omega+\epsilon)\Sigma_{\theta\beta}^{a,<}(\omega+\epsilon)  \end{eqnarray}  They can be reformulated in terms of self-energies as  \begin{eqnarray}  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)