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S(t,t') = S^>(t,t')+S^<(t,t')  \end{equation}  where $S(t,t')=\langle I(t),I(t')\rangle$. Let us consider now the time-ordered $S^t(t,t')$, then  \begin{eqnarray}  &&S^t(t,t´)= \nonumber  \\  &&\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} \begin{multline}  S^t(t,t´)=   \frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma}  V_{\beta k} V_{\gamma q}^{*} \langle T \eta_\beta (t)c_k(t)c_{q}^\dagger(t') \eta_\gamma(t') \rangle   + V_{\beta k}^{*}V_{\gamma q}  \langle T c_{k}^\dagger(t) \eta_\beta(t)\eta_\gamma(t')c_q(t')\rangle \,,  \end{eqnarray} \end{multline}  We apply Wick theorem to $S^t(t,t')$, the  \begin{eqnarray}  &&S^t(t,t´)=\frac{e^2}{\hbar^2}\sum_{k\beta,q\gamma} V_{\beta k} V_{\gamma q}^{*}