deletions | additions       diff --git a/When_applied_an_electric_field__.tex b/When_applied_an_electric_field__.tex  index 7a39687..5c0fb6f 100644  --- a/When_applied_an_electric_field__.tex  +++ b/When_applied_an_electric_field__.tex 
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CDW was modeled as a classical particle moving in a "wash board" potential, which was approximated by parabolic and sinusoidal potentials. The particle was overdamped and subjected to electric force $e E$. Only when the applied DC electric field exceeds some threshold value $E_{th}$ will the CDW "particle" start to "slide", also known as the "depinning" process of CDW \cite{Gr_ner_1981}. Once depinned, the equation of motion for CDW particle can be written in terms of position x or the phase shift $\phi$.   \begin{equation}  \frac{d^{2}\phi}{dt^{2}} + \Gamma \frac{d\phi}{dt} + 2k_F V_0 sin(2k_F \phi) =\frac{e =\frac{e}{m} (E_{dc} +  E_{ac}cos(\omega t)}{m} t))  \end{equation}  where $\Gamma$ is the damping coefficient determined by experiment and m and e are the collective mass and charge of CDW respectively. By varying parameters in equation (5), such as E_{ac} and , one can obtain the "diode-like" conductance of depinned CDW.  
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P \approx exp(-E_0/E)  \end{equation}  The probability comes in the right hand side of equation (5), reducing the force felt by CDW by a fraction of P. The weak electric field, i.e. $E_0 >> E$ leads to vanishing of the force. The Thus the  conductance is negligible. For large field $E >> E_0$, the force is nonlinearly dependent upon E, thus the second term in equation (4) makes sense. shows up.  For weak AC electric fields, CDW oscillates in the potential and remained pinned. There will be no mesurable conductance.