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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{eqnarray}  &&S^>(\omega)=\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} \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 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')}  &&\\ \nonumber \\  \Biggr\{  [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)]\\ \nonumber 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{eqnarray} \end{multline}