Add note about new NV

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@@ -242,6 +242,75 @@ We can look at the Nam conductivity now:
 As there is as yet no filtering based on the free energy, this is messy, so the comparison to \cref{fig:osRepro1b} is necessary to see which combinations of $T$ and $n$ are valid.
 However, this is still quite numerically unstable, even with the dimensional reduction procedure described above for $n$ and $\corr$.
 The information that higher $n$ leads to lower $\sigma$ is expected, and does suggest that the implementation is correct, although still very noisy.
+
+\section{Noise calculation}
+
+For our noise calculation, we assume a material parameterised by a Debye frequency $\debye$ and the interaction parameter $N(0) V$.
+Because these aren't necessarily experimentally accessible, I tried to keep their values such that they lead to a physically reasonable $T_c$.
+In order to keep $N(0) V$ small and $\debye$ bigger than the other parameters, I chose $N(0)V = 0.25$ and $\debye = \SI{1e13}{\per\s}$.
+This leads to $T_{c0} = T_c(\mu = 0) = \SI{1.44e11}{\per\s}$, similar to the values used for the equilibrium Nam case.
+
+Because that particular choice of $N(0) V$ and $\debye$ lead to some additional numerical noise for $T$ close to $T_c$, I changed the values slightly to $N(0) V = 0.2$ and $\debye = \SI{1e14}{\per\s}$, which leads to $T_{c0} = \SI{7.64e11}{\per\s}$, and ensures the graphs below look good for $T > 0.8 T_c$.
+
+\begin{enumerate}
+	\item Use the Owen Scalapino coupled integral equations \cref{eq:gap,eq:n}, find $\mu$ and $\Delta$ for fixed $n$.
+	\item Find the expected gap from the approximation in OS, $T_c(n) \approx (1 - 4n) T_{c0}$.
+	If $T > T_c(n)$, then the calculation is skipped (a more complete handling would use either the Lindhard form or use a Nam expression that's been extended to $\Delta = 0$).
+	This is necessary because the coupled integral equations are very hard to solve
+	\item Using the modified Nam equations, calculate the dielectric function and create the approximated interpolation form, similar to the equilibrium case.
+	\item Calculate the noise as usual.
+\end{enumerate}
+
+\subsection{Figures}
+
+Some examples of the noise are potrayed below, from \crefrange{fig:smallomeganoise}{fig:largerTnoise}.
+There are some interesting features in the graphs:
+\begin{itemize}
+	\item In the curves for constant omega, \crefrange{fig:smallomeganoise}{fig:bigomeganoise}, there seems to be a consistent dip, where initially as $T$ increases, the noise decreases.
+	That seems like it could be an artifact of the method used to calculate $\Delta$, but it is very odd (because nothing besides $\Delta$) should affect any other step.
+	\item In the constant omega graphs, for $n = .02$ and $n = .04$ the noise is greater than for $n = 0$ even in the region where it goes to the `normal state'.
+	This is confusing.
+	\item Most values of $n$ should not be superconducting for most of the range of $T$, as expected.
+	Near the critical temperature for a particular $n$, the noise increases as expected, showing a little gap.
+	See \cref{fig:mediumTnoise}.
+\end{itemize}
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=14cm]{constOmega1/1}
+	\caption{$T_1$ vs temperature, for very small omega} \label{fig:smallomeganoise}
+\end{figure}
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=14cm]{constOmega1/10}
+	\caption{$T_1$ vs temperature, for medium omega} \label{fig:mediumomeganoise}
+\end{figure}
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=14cm]{constOmega1/13}
+	\caption{$T_1$ vs temperature, for big omega} \label{fig:bigomeganoise}
+\end{figure}
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=14cm]{constT1/43}
+	\caption{$T_1$ vs frequency, for a temperature where all the chosen $n$ values are allowed, showing the gap between $n = 0$ and $n > 0$, which seems potentially spurious.} \label{fig:smallTnoise}
+\end{figure}
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=14cm]{constT1/35}
+	\caption{$T_1$ vs frequency, for a temperature where the $n = .04$ state is almost, but not quite surpressed.} \label{fig:mediumTnoise}
+\end{figure}
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=14cm]{constT1/15}
+	\caption{$T_1$ vs frequency, for temperature so large that only the $n = 0$ state is energetically allowed to be superconducting} \label{fig:largerTnoise}
+\end{figure}
+
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