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@@ -271,6 +271,18 @@ The critical points of the 2-spin model are all adjacent: no critical point is s \section{(2 + 4)-spin} +\section{Numerics} + +To confirm the presence of Stokes lines under certain processes in the $p$-spin, we studied the problem numerically. +\begin{equation} + \mathcal L(z(t), z'(t)) + = 1-\frac{\operatorname{Re}(\dot z^*_iz'_i)}{|\dot z||z'|} +\end{equation} +\begin{equation} + \mathcal C[\mathcal L]=\int dt\,\mathcal L(z(t), z'(t)) +\end{equation} +$\mathcal C$ has minimum of zero, which is reached only by functions $z(t)$ whose tangent is everywhere parallel to the direction of the dynamics. Therefore, finding functions which reach this minimum will find time-reparameterized Stokes lines. For the sake of numeric stability, we look for functions whose tangent has constant norm. + \begin{acknowledgments} MIT mathematicians have been no help \end{acknowledgments} |