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Pierre-Francois Loos 2020-06-01 22:44:00 +02:00
parent f61c78f3bd
commit 216d5c3ab4
1 changed files with 4 additions and 4 deletions
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BSEdyn.tex
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@ -536,7 +536,7 @@ From a more practical point of view, to compute the BSE excitation energies of a
\begin{pmatrix} \begin{pmatrix}
\bA{}(\Om{s}{}) & \bB{}(\Om{s}{}) \bA{}(\Om{s}{}) & \bB{}(\Om{s}{})
\\ \\
-\bB{}(\titou{-}\Om{s}{}) & -\bA{}(\titou{-}\Om{s}{}) -\bB{}(\Om{s}{}) & -\bA{}(\Om{s}{})
\\ \\
\end{pmatrix} \end{pmatrix}
\cdot \cdot
@ -581,7 +581,7 @@ Now, let us decompose, using basic perturbation theory, the non-linear eigenprob
\label{eq:LR-PT} \label{eq:LR-PT}
\begin{pmatrix} \begin{pmatrix}
\bA{}(\Om{s}{}) & \bB{}(\Om{s}{}) \\ \bA{}(\Om{s}{}) & \bB{}(\Om{s}{}) \\
-\bB{}(\titou{-}\Om{s}{}) & -\bA{}(\titou{-}\Om{s}{}) \\ -\bB{}(\Om{s}{}) & -\bA{}(\Om{s}{}) \\
\end{pmatrix} \end{pmatrix}
\\ \\
= =
@ -594,7 +594,7 @@ Now, let us decompose, using basic perturbation theory, the non-linear eigenprob
+ +
\begin{pmatrix} \begin{pmatrix}
\bA{(1)}(\Om{s}{}) & \bB{(1)}(\Om{s}{}) \\ \bA{(1)}(\Om{s}{}) & \bB{(1)}(\Om{s}{}) \\
-\bB{(1)}(\titou{-}\Om{s}{}) & -\bA{(1)}(\titou{-}\Om{s}{}) \\ -\bB{(1)}(\Om{s}{}) & -\bA{(1)}(\Om{s}{}) \\
\end{pmatrix}, \end{pmatrix},
\end{multline} \end{multline}
with with
@ -675,7 +675,7 @@ Thanks to first-order perturbation theory, the first-order correction to the $s$
\cdot \cdot
\begin{pmatrix} \begin{pmatrix}
\bA{(1)}(\Om{s}{(0)}) & \bB{(1)}(\Om{s}{(0)}) \\ \bA{(1)}(\Om{s}{(0)}) & \bB{(1)}(\Om{s}{(0)}) \\
-\bB{(1)}(\titou{-}\Om{s}{(0)}) & -\bA{(1)}(\titou{-}\Om{s}{(0)}) \\ -\bB{(1)}(\Om{s}{(0)}) & -\bA{(1)}(\Om{s}{(0)}) \\
\end{pmatrix} \end{pmatrix}
\cdot \cdot
\begin{pmatrix} \begin{pmatrix}