From 95a311392775786d4cafc10d8ec424a7f3a0d09f Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Tue, 20 Jun 2023 08:04:44 +0200 Subject: Small tweaks. --- 2-point.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/2-point.tex b/2-point.tex index b596e3b..22cce5b 100644 --- a/2-point.tex +++ b/2-point.tex @@ -962,7 +962,7 @@ m)=E_\mathrm{th}$, the threshold energy is also the pivot around which the points asymptotically nearby marginal minima change their properties. To examine better the population of marginal points, it is necessary to look at -the next term in the series of the complexity with $\delta q$, since the linear +the next term in the series of the complexity with $\Delta q$, since the linear coefficient becomes zero at the marginal line. This tells us something intuitive: stable minima have an effective repulsion between points, and one always finds a sufficiently small $\Delta q$ that no stationary points are @@ -988,7 +988,7 @@ where $\delta\mu_1$ is given by the coefficient in \eqref{eq:expansion.mu.1} and \begin{equation} \delta\mu_2=\frac{v_f}{f'(1)f''(1)^{3/4}}\sqrt{ - \frac{E_0-E_\mathrm{th}}2\frac{f'(1)\big(f'''(1)-2f''(1)\big)+2f''(1)^2}{u_f} + \frac{E_0-E_\mathrm{th}}2\frac{2f''(1)\big(f''(1)-f'(1)\big)+f'(1)f'''(1)}{u_f} } \end{equation} Similarly, one finds that the energy lies in the range $E_1=E_0+\delta -- cgit v1.2.3-70-g09d2