From bcae81336764eb6c4cdf0f91e2fe632b625dd8b2 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Sun, 23 Oct 2022 22:18:11 +0200
Subject: Optimize and improve naming of all images in knowledge base
---
source/know/concept/random-phase-approximation/index.md | 16 ++++------------
1 file changed, 4 insertions(+), 12 deletions(-)
(limited to 'source/know/concept/random-phase-approximation/index.md')
diff --git a/source/know/concept/random-phase-approximation/index.md b/source/know/concept/random-phase-approximation/index.md
index 0f53136..698e1e7 100644
--- a/source/know/concept/random-phase-approximation/index.md
+++ b/source/know/concept/random-phase-approximation/index.md
@@ -71,23 +71,17 @@ leaving only the single most divergent one at each order $$n$$,
i.e. the ones where all $$n$$ interaction lines
carry the same momentum and energy:
-
-
-
+{% include image.html file="self-energy.png" width="92%" alt="RPA self-energy definition" %}
Where we have defined the **screened interaction** $$W^\mathrm{RPA}$$,
denoted by a double wavy line:
-
-
-
+{% include image.html file="interaction.png" width="95%" alt="RPA screened interaction definition" %}
Rearranging the above sequence of diagrams quickly leads to the following
[Dyson equation](/know/concept/dyson-equation/):
-
-
-
+{% include image.html file="dyson.png" width="55%" alt="Dyson equation for screened interaction" %}
In Fourier space, this equation's linear shape
means it is algebraic, so we can write it out:
@@ -104,9 +98,7 @@ with an internal wavevector $$\vb{q}$$, fermionic frequency $$i \omega_m^F$$, an
Abbreviating $$\tilde{\vb{k}} \equiv (\vb{k}, i \omega_n^B)$$
and $$\tilde{\vb{q}} \equiv (\vb{q}, i \omega_n^F)$$:
-
-
-
+{% include image.html file="pairbubble.png" width="45%" alt="Internal variables of pair-bubble diagram" %}
We isolate the Dyson equation for $$W^\mathrm{RPA}$$,
which reveals its physical interpretation as a *screened* interaction:
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