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Rosa edited untitled.tex
about 8 years ago
Commit id: 5185064b49534f051bab6d4bb283b2f775cef6b7
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index 66e2e76..a3da748 100644
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\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}\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 + V_{\alpha p} g^{h,<}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta
\gamma}(\epsilon)[V^*_{\beta \gamma}(\epsilon)[V_{\beta k}
g_{q}^{h,<}(\omega+\epsilon)V_{\gamma g_{q}^{h,<}(\omega+\epsilon)V^*_{\gamma q}\delta_{kq}
\end{eqnarray}
\begin{eqnarray}
S^{>,2}(\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 + V_{\alpha p} g^{h,<}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon)
[V^*_{\beta [V_{\beta k} g_{k}^{h,r}(\omega+\epsilon) V_{\gamma k} G^{<}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^*
g_{q}^{h,a}(\omega+\epsilon)V_{\gamma g_{q}^{h,a}(\omega+\epsilon)V^*_{\gamma q}]
\end{eqnarray}
\begin{eqnarray}
S^{>,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 + V_{\alpha p} g^{h,<}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon)
[V^*_{\beta [V_{\beta k} g_{k}^{h,r}(\omega+\epsilon) V_{\gamma k} G^{<}_{\gamma\beta}(\omega+\epsilon)V_{\beta q}^*
g_{q}^{h,a}(\omega+\epsilon)V_{\gamma g_{q}^{h,a}(\omega+\epsilon) V^*_{\gamma q}]
\end{eqnarray}
\begin{eqnarray}
S^{>,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 + V_{\alpha p} g^{h,<}_{p}(\epsilon) V^*_{\delta p}] G^a_{\delta
\gamma}(\epsilon)[V^*_{\beta \gamma}(\epsilon)[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 g_{q}^{h,a}(\omega+\epsilon)V^*_{\gamma q}]
\end{eqnarray}