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\end{equation}  \begin{multline}  S^>(\omega)=\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} \frac{1}{2\pi}\int_{-\infty}^\inftyd\omega \frac{1}{2\pi}\int_{-\infty}^\infty  d\epsilon \\   \Biggr\{  V_{\beta k} V_{\gamma q}^{*} [G^>_{\beta\gamma}(\epsilon) G^{h,<}_{qk}(\omega+\epsilon) - G^{>}_{\beta q}(\epsilon)G^{h,<}_{\gamma k}(\epsilon+\omega)] 
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\end{eqnarray}  On the other hand we have for $G^>_{\beta\gamma}(\epsilon)$ (accordingly with J.S note)  \begin{eqnarray}  G^>_{\beta\gamma}(\epsilon) = \sum_{k\alpha\delta}\int \frac{d\epsilon}{2\pi}  G^r_{\beta \alpha}(\epsilon) [V^*_{k\alpha} g^<_{k}(\epsilon)V_{k\delta} + V_{k\alpha} g^{h,<}_{k}(\epsilon) V^*_{k\delta}]G^a_{\delta \gamma}(\epsilon) \end{eqnarray}  We need to compute the following product of Green functions: $G^>_{\beta\gamma}(\epsilon)G_{kq}^{h,<}(\omega+\epsilon)$  \begin{eqnarray}  &&G^>_{\beta\gamma}(\epsilon) G_{kq}^{h,<}(\omega+\epsilon) = \sum_{k\alpha\delta}\int \frac{d\omega}{2\pi}  G^r_{\beta \alpha}(\epsilon) [V^*_{k\alpha} g^<_{k}(\omega)V_{k\delta} + V_{k\alpha} g^{h,<}_{k}(\omega) V^*_{k\delta}]G^a_{\delta \gamma}(\epsilon) g_{q}^{h,<}(\omega+\epsilon)\delta_{kq} \\ \nonumber &+& \sum_{p\beta\gamma\alpha\gamma}\int \frac{d\omega}{2\pi} \sum_{p\beta\gamma\alpha\gamma}  G^r_{\beta \alpha}(\epsilon) [V^*_{p\alpha} g^<_{p}(\epsilon)V_{p\delta} + V_{p\alpha} g^{h,<}_{p}(\epsilon) V^*_{p\delta}]G^a_{\delta \gamma}(\epsilon) [g_{k}^{h,r}(\omega+\epsilon) V_{\gamma k} G^{r}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{h,<}(\omega) \nonumber \\  &&+G^r_{\beta \alpha}(\epsilon) [V^*_{p\alpha} g^<_{p}(\epsilon)V_{p\delta} + V_{p\alpha} g^{h,<}_{p}(\epsilon) V^*_{p\delta}]G^a_{\delta \gamma}(\epsilon) [g_{k}^{h,r}(\omega+\epsilon) V_{\gamma k} G^{<}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{h,a}(\omega+\epsilon)]\\ \nonumber  &&+G^r_{\beta \alpha}(\epsilon) [V^*_{p\alpha} g^<_{p}(\epsilon)V_{p\delta} + V_{p\alpha} g^{h,<}_{p}(\epsilon) V^*_{p\delta}]G^a_{\delta \gamma}(\epsilon)[g_{k}^{h,<}(\omega+\epsilon) V_{\gamma k} G^{a}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^* g_{q}^{h,a}(\omega+\epsilon)]\,,  \end{eqnarray}  We now compute separately the different parts of the previous expression for the ac noise  \begin{eqnarray}  S^{>,1}(\omega)= \frac{e^2}{\hbar^2}\sum_{p\beta,q\gamma} \frac{1}{2\pi}\int_{-\infty}^\infty d\epsilon \sum_{k,q\beta\gamma\alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{p\alpha} g^<_{p}(\omega)V_{p\delta} + V_{p\alpha} g^{h,<}_{p}(\omega) V^*_{k\delta}]G^a_{\delta \gamma}(\epsilon) g_{q}^{h,<}(\omega+\epsilon)\delta_{kq}  \end{eqnarray}