From 49934b54a919f6e10fef2f33a934958415eaf40c Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 2 Feb 2022 22:01:12 +0100
Subject: Tweaked first figure, and added another depicting a Stokes point.

---
 stokes.tex | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

(limited to 'stokes.tex')

diff --git a/stokes.tex b/stokes.tex
index 4c1a882..6485ed7 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -257,6 +257,26 @@ called \emph{Stokes points}, and the gradient descent trajectories that join
 two stationary points are called \emph{Stokes lines}. An example of this
 behavior can be seen in Fig.~\ref{fig:1d.stokes}.
 
+\begin{figure}
+  \includegraphics{figs/thimble_stokes_1.pdf}\hfill
+  \includegraphics{figs/thimble_stokes_2.pdf}\hfill
+  \includegraphics{figs/thimble_stokes_3.pdf}
+
+  \caption{
+    An example of a Stokes point. (Left) The collection of thimbles necessary
+    to progress around from left to right, highlighted in a darker color, is
+    the same as it was in Fig.~\ref{fig:thimble.homology}. (Center) The thimble
+    $\mathcal J_\blacklozenge$ intersects the stationary point $\blacktriangle$
+    and its thimble, leading to a situation where the contour is not easily
+    defined using thimbles. This is a Stokes point. (Right) The Stokes point
+    has passed, and the collection of thimbles necessary to produce the path
+    has changed: now $\mathcal J_\blacktriangle$ must be included. Notice that
+    in this figure, because of the symmetry of the pure models, the thimble
+    $\mathcal J_\blacksquare$ also experiences a Stokes point, but this does
+    not result in a change to the path involving that thimble.
+  } \label{fig:1d.stokes}
+\end{figure}
+
 The prevalence (or not) of Stokes points in a given continuation, and whether
 those that do appear affect the weights of critical points of interest, is a
 concern for the analytic continuation of theories. If they do not occur or
-- 
cgit v1.2.3-70-g09d2

