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...
\end{equation}
Now we compute the lead-lead Green function $G^{t,h}_{kq}(t,t')=\langle T c_k^\dagger(t) c_q(t')\rangle$ that appears in the previous expression. We compute its equation-of-motion
\begin{equation}
i\hbar \partial_{t'}
G_{kq}^{h,t}(t,t') G_{kq}^{t,h}(t,t') = \epsilon_q G_{kq}^{t,h}(t,t') + \sum_\beta V_{\beta q}^*
G^{h,t}_{k\beta}(t,t') G^{t,h}_{k\beta}(t,t')
\end{equation}
Then we get
\begin{equation}
G_{kq}^{t,h}(t,t') = G_{kq}^{t,h}(t,t')\delta_{kq} + \frac{-1}{\hbar} \sum_\tau\int dt_1 G^{t,h}_{k\tau}(t,t')V_{\tau q}^* g_{q}^{t,h}(t_1,t')
\end{equation}
In a similar way we can obtain the mixed (hole) lead-Majorana Green function
$G_{k\beta}^{t,h}{t,t'}$ $G_{k\beta}^{t,h}(t,t')$
\begin{equation}
G_{k\tau}^{t,h}(t,t') = \frac{-1}{\hbar} \sum_{\theta}\int dt_1 g_{k}^{t,h}(t,t_1) V_{\theta k} G^{t}_{\theta\tau}(t,t')
\end{equation}
Then, inserting the previous expression into the equation for $G_{qk}^{h,t}(t,t')$, we obtain
\begin{equation}
G_{qk}^{h,t}(t,t') G_{qk}^{t,h}(t,t') =
G_{qk}^{h,t}(t,t')\delta_{kq} G_{qk}^{t,h}(t,t')\delta_{kq} + \sum_{\tau\theta}\int \frac{-dt_1}{\hbar}\frac{-dt_2}{\hbar}
g_{q}^{h,t}(t,t_1) g_{q}^{t,h}(t,t_1) V_{\tau q} G^{t}_{\tau\theta}(t_1,t_2)V_{\theta k}^*
g_{k}^{h,t}(t_2,t') g_{k}^{t,h}(t_2,t')
\end{equation}
The rest of equations for the Green functions that appear in the noise expression are already in J. S note.
Now we employ the following definition for the Fourier transform
...
Now we enter the expression for $G_{kq}^{t,h}(t,t')$ in the frequency domain
\begin{equation}
G_{qk}^{h,t}(\omega) G_{qk}^{t,h}(\omega) = g_{q}^{t,h}(\omega)\delta_{kq} + \sum_{\tau\theta} g_{q}^{t,h}(\omega) V_{\tau q} G^{t}_{\tau\theta}(\omega)V_{\theta k}^* g_{k}^{t,h}(\omega)\,,
\end{equation}
\begin{multline}
S^>(\omega)=\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} \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^{<,h}_{qk}(\omega+\epsilon) - G^{>}_{\beta
q}(\epsilon)G^{h,<}_{\gamma q}(\epsilon)G^{<,h}_{\gamma k}(\epsilon+\omega)]
+ V_{\beta k}^{*}V_{\gamma q} [G^{>,h}_{kq}(\epsilon_1)
G^{<}_{\gamma\beta}(\epsilon+\omega) G^{>,h}_{\gamma\beta}(\epsilon+\omega) -
G^{h,>}_{k\gamma}(\epsilon)G^{<}_{q G^{>,h}_{k\gamma}(\epsilon)G^{<}_{q \beta}(\epsilon+\omega)]\Biggr\}\,,
\end{multline}
Let us treat first the following term: $e^2/\hbar^2\sum_{k\beta,q\gamma} V_{\beta k} V_{\gamma q}^{*} [G^>_{\beta\gamma}(\epsilon)
G^{h,<}_{qk}(\omega+\epsilon)]$ G^{<,h}_{qk}(\omega+\epsilon)]$
Then,
\begin{eqnarray}
&&G_{qk}^{h,<}(\omega+\epsilon) &&G_{qk}^{<,h}(\omega+\epsilon) =
g_{q}^{h,<}(\omega+\epsilon)\delta_{kq} g_{q}^{<,h}(\omega+\epsilon)\delta_{kq} + \sum_{\tau\theta}
[g_{q}^{h,r}(\omega+\epsilon) [g_{q}^{r,h}(\omega+\epsilon) V_{\tau q} G^{r}_{\tau\theta}(\omega+\epsilon)V_{\theta k}^*
g_{k}^{h,<}(\omega)\nonumber g_{k}^{<,h}(\omega)\nonumber
\\
&&+g_{q}^{h,r}(\omega+\epsilon) &&+g_{q}^{r,h}(\omega+\epsilon) V_{\tau q} G^{<}_{\tau\theta}(\omega+\epsilon)V_{\theta k}^*
g_{k}^{h,a}(\omega+\epsilon)+g_{q}^{h,<}(\omega+\epsilon) g_{k}^{a,h}(\omega+\epsilon)+g_{q}^{<,h}(\omega+\epsilon) V_{\tau q} G^{a}_{\tau\theta}(\omega+\epsilon)V_{\theta k}^*
g_{k}^{h,a}(\omega+\epsilon)\,, g_{k}^{a,h}(\omega+\epsilon)\,,
\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_{p\alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^>_{p}(\epsilon)V_{\delta p} + V_{\alpha p}
g^{h,>}_{p}(\epsilon) g^{>,h}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon)
\end{eqnarray}
We need to compute the following product of Green functions: $P^>(t,t')=e^2/\hbar^2\sum_{k\beta,q\gamma}
G^>_{\beta\gamma}(\epsilon)G_{kq}^{h,<}(\omega+\epsilon)$ V_{\beta k}V^*_{\gamma q} G^>_{\beta\gamma}(\epsilon)G_{kq}^{<,h}(\omega+\epsilon)$
\begin{align*}
&\sum_{k\alpha\delta} & \sum_{k q\beta\gamma} V_{\gamma q}^* V_{\beta k} G^>_{\beta\gamma}(\epsilon)
G_{kq}^{h,<}(\omega+\epsilon) G_{kq}^{<,h}(\omega+\epsilon) =
\sum_{k\alpha\delta} \sum_{k,p,q \beta \alpha\delta \gamma} \Biggr\{ V_{\gamma q}^* V_{\beta
k}\Biggr\{ k} G^r_{\beta \alpha}(\epsilon)
[V^*_{k\alpha} g^>_{k}(\epsilon)V_{\delta k} [V^*_{p\alpha} g^>_{p}(\epsilon)V_{\delta p} + V_{\alpha
k} g^{h,>}_{k}(\epsilon) p} g^{>,h}_{p}(\epsilon) V^*_{\delta
k}]G^a_{\delta p}]G^a_{\delta \gamma}(\epsilon)
g_{q}^{h,<}(\omega+\epsilon)\delta_{kq} g_{q}^{<,h}(\omega+\epsilon)\delta_{kq} \\ \nonumber
&+
\sum_{p \alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^>_{p}(\epsilon)V_{ \delta}p + V_{\alpha p}
g^{h,>}_{p}(\epsilon) g^{>,h}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon) [ V_{\gamma q}^*
g_{q}^{h,r}(\omega+\epsilon) g_{q}^{r,h}(\omega+\epsilon) V_{\tau q} G^{r}_{\tau\theta}(\omega+\epsilon)V_{\theta k}^*
g_{k}^{h,<}(\omega) g_{k}^{<,h}(\omega) V_{\beta k} \nonumber
\\
&\sum_{p \alpha\delta} & + G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^>_{p}(\epsilon)V_{ \delta}p + V_{\alpha p}
g^{h,>}_{p}(\epsilon) g^{>,h}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon) [ V_{\gamma q}^*
g_{q}^{h,r}(\omega+\epsilon) g_{q}^{r,h}(\omega+\epsilon) V_{\tau q} G^{<}_{\tau\theta}(\omega+\epsilon)V_{\theta k}^*
g_{k}^{h,a}(\omega) g_{k}^{a,h}(\omega) V_{\beta k}
\nonumber
\\
&+ \sum_{p \alpha\delta} G^r_{\beta \alpha}(\epsilon) [V^*_{\alpha p} g^>_{p}(\epsilon)V_{ \delta}p + V_{\alpha p}
g^{h,>}_{p}(\epsilon) g^{>,h}_{p}(\epsilon) V^*_{\delta p}]G^a_{\delta \gamma}(\epsilon) [ V_{\gamma q}^*
g_{q}^{h,<}(\omega+\epsilon) g_{q}^{<,h}(\omega+\epsilon) V_{\tau q} G^{a}_{\tau\theta}(\omega+\epsilon)V_{\theta k}^*
g_{k}^{h,a}(\omega) g_{k}^{a,h}(\omega) V_{\beta k} \Biggr\}
\,,
\end{align*}
We now compute separately the different parts of the previous expression for the ac noise
