deletions | additions       diff --git a/When_applied_an_electric_field__.tex b/When_applied_an_electric_field__.tex  index 9556f73..a8fdc35 100644  --- a/When_applied_an_electric_field__.tex  +++ b/When_applied_an_electric_field__.tex 
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P \approx exp(-E_0/E)  \end{equation}  Where $E_0$ is the function of the gap energy. The probability comes in the right hand side of equation (5), reducing the force felt by CDW by a fraction of P. $P$.  \begin{equation}  \frac{d^{2}\phi}{dt^{2}} + \Gamma \frac{d\phi}{dt} + 2k_F V_0 sin(2k_F \phi) =\frac{e}{m} E_{dc} exp(-E_0/E_{dc})  \end{equation}  The weak electric field, i.e. $E_0 >> E$ E_{dc}$  leads to vanishing of the force. Thus the conductance is negligible. For large field $E $E_{dc}  >> E_0$, the force is nonlinearly dependent upon E, $E_{dc}$,  thus the second term in equation (4) shows up. Moreover, the different lattice spacing gives rise to different values of gap energy. The constant in the exponent, $E_0$, depends upon the gap energy; therefore, the relationship between the lattice spacing and the threshold electric field will also be investigated. Secondly, this project will investigate the relationship between the AC conductance and the frequency of applied field. This problem was dealt with by considering the classical single particle model. For very high or very low frequency, the AC conductance vanishes since CDW is overdamped. The AC conductance plays an important role if the frequency is near the frequency of CDW. In this case from equation (1) 
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\omega_0 = 2k_F v  \end{equation}  The resonance of the applied AC field and CDW occurs at $\omega \approx \omega_0$, where the electric field shifts CDW by a one  distorted lattice spacing within one period. The resonance frequency is determined by the gap energy and also the period of the potential.