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 Binary files /dev/null and b/source/know/concept/random-phase-approximation/pairbubble.avif differ 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 Binary files a/source/know/concept/random-phase-approximation/screened.png and /dev/null differ 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 -- cgit v1.2.3