deletions | additions       diff --git a/Intro.tex b/Intro.tex  index a01b76e..585b17f 100644  --- a/Intro.tex  +++ b/Intro.tex 
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\[ P_n(t) = \avg{\mu \rho_n(t)} \]  I wish to use a general form to relate the polarization measurement $P_3(t)$ with n\ts{th} order perturbations of the density matrix. In superoperator form (where the elements of $n\times n$ density matrices concatenate to create $1\times n^2$ vectors), let us define $x$ $\v{x}$  as a concatenation of $\rho_n, 0\le n\le 3$: \[ x(t) \v{x}(t)  = \left( \begin{array}{cccc} \rho_0(t) \\  \rho_1(t) \\  \rho_2(t) \\ 
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0 \\  0 \\  F \\  \end{array}\right) \cdot x(t)\] \v{x}(t)\]  such that applying $F$ (in operator form) behaves as follows: $F \cdot = \avg{\mu \cdot}$. The $1\times 4n^2$ vector $x(t)$ $\v{x}(t)$  is governed by the time evolution equation \[ \pd{x(t)}{t} \pd{\v{x}(t)}{t}  = \left( \begin{array}{cccc} 0 & 0 & 0 & 0 \\  A(t) & 0 & 0 & 0 \\  0 & A(t) & 0 & 0 \\  0 & 0 & A(t) & 0 \\  \end{array} \right) x(t) \v{x}(t)  \] where $x(0) $\v{x}(0)  = \left( \begin{array}{cccc} \rho(0) \\  0 \\  0 \\