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with the total noise as $S=S^A+S^B+S^C$  No we compute the second contribution to the noise from $N(t,t')=(e^2/h)\sum_{k\beta,q\gamma} V_{\beta k} V^*_{\gamma q}G_{\beta q}>(t,t') G^{h,<}_{\gamma k}(t',t)$. These two Green functions read  \begin{eqnarray}  G^>_{\beta q^)(t,t') qÇ(t,t')  = \frac{1}{h} \sum_\gamma \int dt_1 [G_{\beta\gamma}^r(t,t_1) V_{\gamma q} g^{>}_{q}(t_1,t')+ G_{\beta\gamma}^>(t,t_1) V_{\gamma q} g^{a}_{q}(t_1,t') \end{eqnarray}  \begin{eqnarray}  G^{<,h}_{\gamma k^)(t,t') k^}(t,t')  = \frac{-1}{h} \sum_\beta \int dt_1 [G_{\gamma\beta}^r(t',t_1) V_{\beta k} g^{<,h}_{k}(t_1,t)+ G_{\gamma\beta}^<(t',t_1) V_{\beta k} g^{a,h}_{k}(t_1,t) \end{eqnarray}  In the frequency domain the product of these two functions read:  \begin{eqnarray} 
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\end{eqnarray}  where  \begin{eqnarray}  G^>_{\beta q^)(\omega+\epsilon) q^}(\omega+\epsilon)  = \sum_\gamma [G_{\beta\gamma}^r(\omega+\epsilon) V_{\gamma q} g^{>}_{q}(\omega+\epsilon)+ G_{\beta\gamma}^>(\omega+\epsilon) V_{\gamma q} g^{a}_{q}(\omega+\epsilon)] \end{eqnarray}  \begin{eqnarray}  G^{<,h}_{\gamma k^)(\omega) k^}(\omega)  = \sum_\beta [G_{\gamma\beta}^r(\omega) V_{\beta k} g^{<,h}_{k}(\omega)+ G_{\gamma\beta}^<(\omega) V_{\beta k} g^{a,h}_{k}(\omega)] \end{eqnarray}