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
---
.../know/concept/random-phase-approximation/dyson.avif | Bin 0 -> 3017 bytes
source/know/concept/random-phase-approximation/index.md | 16 ++++------------
.../concept/random-phase-approximation/interaction.avif | Bin 0 -> 4946 bytes
.../concept/random-phase-approximation/interaction.png | Bin 0 -> 7338 bytes
.../concept/random-phase-approximation/pairbubble.avif | Bin 0 -> 3558 bytes
.../concept/random-phase-approximation/rpasigma.png | Bin 10310 -> 0 bytes
.../concept/random-phase-approximation/screened.png | Bin 7338 -> 0 bytes
.../concept/random-phase-approximation/self-energy.avif | Bin 0 -> 7165 bytes
.../concept/random-phase-approximation/self-energy.png | Bin 0 -> 10310 bytes
9 files changed, 4 insertions(+), 12 deletions(-)
create mode 100644 source/know/concept/random-phase-approximation/dyson.avif
create mode 100644 source/know/concept/random-phase-approximation/interaction.avif
create mode 100644 source/know/concept/random-phase-approximation/interaction.png
create mode 100644 source/know/concept/random-phase-approximation/pairbubble.avif
delete mode 100644 source/know/concept/random-phase-approximation/rpasigma.png
delete mode 100644 source/know/concept/random-phase-approximation/screened.png
create mode 100644 source/know/concept/random-phase-approximation/self-energy.avif
create mode 100644 source/know/concept/random-phase-approximation/self-energy.png
(limited to 'source/know/concept/random-phase-approximation')
diff --git a/source/know/concept/random-phase-approximation/dyson.avif b/source/know/concept/random-phase-approximation/dyson.avif
new file mode 100644
index 0000000..dc80856
Binary files /dev/null and b/source/know/concept/random-phase-approximation/dyson.avif differ
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:
diff --git a/source/know/concept/random-phase-approximation/interaction.avif b/source/know/concept/random-phase-approximation/interaction.avif
new file mode 100644
index 0000000..f3f6cbe
Binary files /dev/null and b/source/know/concept/random-phase-approximation/interaction.avif differ
diff --git a/source/know/concept/random-phase-approximation/interaction.png b/source/know/concept/random-phase-approximation/interaction.png
new file mode 100644
index 0000000..bb5ccdd
Binary files /dev/null and b/source/know/concept/random-phase-approximation/interaction.png differ
diff --git a/source/know/concept/random-phase-approximation/pairbubble.avif b/source/know/concept/random-phase-approximation/pairbubble.avif
new file mode 100644
index 0000000..bca964e
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diff --git a/source/know/concept/random-phase-approximation/rpasigma.png b/source/know/concept/random-phase-approximation/rpasigma.png
deleted file mode 100644
index fedc9f5..0000000
Binary files a/source/know/concept/random-phase-approximation/rpasigma.png and /dev/null differ
diff --git a/source/know/concept/random-phase-approximation/screened.png b/source/know/concept/random-phase-approximation/screened.png
deleted file mode 100644
index bb5ccdd..0000000
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diff --git a/source/know/concept/random-phase-approximation/self-energy.avif b/source/know/concept/random-phase-approximation/self-energy.avif
new file mode 100644
index 0000000..3ddfed7
Binary files /dev/null and b/source/know/concept/random-phase-approximation/self-energy.avif differ
diff --git a/source/know/concept/random-phase-approximation/self-energy.png b/source/know/concept/random-phase-approximation/self-energy.png
new file mode 100644
index 0000000..fedc9f5
Binary files /dev/null and b/source/know/concept/random-phase-approximation/self-energy.png differ
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