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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  \begin{equation}  F(t-t')=\frac{1}{2\pi}\int_{\infty}^\infty} F(t-t')=\frac{1}{2\pi}\int_{-\infty}^\infty}  d\omega e^{-i\omega t} F(\omega)\,, \end{equation}  Then, the ac spectral noise becomes  \begin{multline}  S^>(\omega)=\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} V_{\beta k} V_{\gamma q}^{*}\frac{1}{2\pi}\int_{-\infty}^\infty \frac{1}{2\pi}\int_{-\infty}^\infty  d\omega e^{-i\omega (t-t')} \frac{1}{2\pi}\int_{-\infty}^\infty d\epsilon_1 e^{-i\epsilon (t-t')} \frac{1}{2\pi}\int_{-\infty}^\infty d\epsilon_2 e^{i\epsilon (t-t')}  \\   \Biggr\{  [G^t_{\beta\gamma}(\epsilon_1) [V_{\beta k} V_{\gamma q}^{*} G^t_{\beta\gamma}(\epsilon_1)  G^{h,t}_{qk}(\epsilon_2) - G^{t}_{\beta q}(\epsilon_1)G^{h,t}_{\gamma k}(\epsilon_2)] + V_{\beta k}^{*}V_{\gamma q} [G^{h,t}_{kq}(\epsilon_1) G{t}_{\gamma\beta}(\epsilon_2) - G^{h,t}_{k\gamma}(\epsilon_1)G^{t}_{q \beta}(\epsilon_2)]\Biggr\}\,,  \end{multline}