deletions | additions       diff --git a/The Peierls Transition.tex b/The Peierls Transition.tex  index ca2dc6d..0eb003f 100644  --- a/The Peierls Transition.tex  +++ b/The Peierls Transition.tex 
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\begin{equation}  \delta u_i = (-1)^{i} \delta a \sin{\omega t}  \end{equation}  where $\delta a$ represents the displacement amplitude, the CDW state will then take place. Such coherence can be achieved by 2D or 3D materials with 1D conducting chains of weak interactions coupling  among neighboring chains.