deletions | additions       diff --git a/untitled.tex b/untitled.tex  index bca8e4b..93e762d 100644  --- a/untitled.tex  +++ b/untitled.tex 
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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} \begin{eqnarray}  S^{>,2}(\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}(\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)]  \end{eqnarray}  \begin{eqnarray}  S^{>,3}(\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}(\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)]  \end{eqnarray}  \begin{eqnarray}  S^{>,4}(\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}(\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}