From 70d9521b3ee04635857211b2aedd783f41c841f8 Mon Sep 17 00:00:00 2001 From: AntoineMarie2 Date: Mon, 20 Jul 2020 13:42:18 +0200 Subject: [PATCH] update sec 5.1 --- RapportStage/Rapport.tex | 24 +++++++++++++++++++----- 1 file changed, 19 insertions(+), 5 deletions(-) diff --git a/RapportStage/Rapport.tex b/RapportStage/Rapport.tex index b31a4c0..f8fee7a 100644 --- a/RapportStage/Rapport.tex +++ b/RapportStage/Rapport.tex @@ -540,13 +540,27 @@ In addition, we can also consider the symmetry-broken solutions beyond their res \subsection{Evolution of the radius of convergence} -Different partitioning +In this part, we will try to investigate how some parameters of $\bH(\lambda)$ influence the radius of convergence of the perturbation series. The radius of convergence is equal to the closest singularity to the origin of $E(\lambda)$. The exceptional points are simultaneous solution of \eqref{eq:PolChar} and \eqref{eq:DPolChar} so we solve this system to find their position. -$Y_{l0}$ vs $P_l(\cos(\theta))$ +\begin{equation}\label{eq:PolChar} +\text{det}[E-\bH(\lambda)]=0 +\end{equation} + +\begin{equation}\label{eq:DPolChar} +\pdv{E}\text{det}[E-\bH(\lambda)]=0 +\end{equation} + +We will take the simple case of the M{\o}ller-Plesset partitioning with a restricted Hartree-Fock minimal basis set as our starting point for this analysis. \\ + +Puis on rajoute les 3 autres partitionnements \\ + +Puis différence entre $Y_{l0}$ et $P_l(\cos(\theta))$ (CSF). Parler de la possibilité de la base strong coupling. \\ + +Différence RHF/UHF, Hamiltonien non-bloc diagonal, coefficients complexe pour R<3/2 \\ + +Influence de la taille de la base en RHF et UHF \\ -Size of the basis set -Strong coupling ??? \subsection{Exceptional points in the UHF formalism} @@ -562,7 +576,7 @@ PT broken symmetry sb UHF \begin{itemize} \item Corriger les erreurs dans la biblio -\item tableau nrj uhf, citation spin density wave et charge density wave +\item citation spin density wave et charge density wave \end{itemize} \section{Conclusion}