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\subsection{AC Conductivity}  If the applied voltage is a small pure AC signal with $V_{dc}=0$ and $|V_{ac}|DC  conductivity appears as the frequency $\omega$ is increased and exceeds certain threshold frequency $\omega_t$. This effect is the photon-assisted tunneling of CDW. The electrons in CDW absorbs the oscillating electromagnetic waves within the channel and gains enough energy to tunnel through the gap $\mathcal{E}_g$, giving the finite conductivity above $\omega_t$. From the previous result for DC, \begin{equation}  \sigma(V_{dc})=\sigma_0+\sigma_{dc}\space \left( 1-\frac{V_t}{V_{dc}}\right) \space exp \left( -\frac{V_0}{V_{dc}} \right)  \end{equation}