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Diffstat (limited to 'source/know/concept/random-phase-approximation')
| -rw-r--r-- | source/know/concept/random-phase-approximation/dyson.avif | bin | 0 -> 3017 bytes | |||
| -rw-r--r-- | source/know/concept/random-phase-approximation/index.md | 16 | ||||
| -rw-r--r-- | source/know/concept/random-phase-approximation/interaction.avif | bin | 0 -> 4946 bytes | |||
| -rw-r--r-- | source/know/concept/random-phase-approximation/interaction.png (renamed from source/know/concept/random-phase-approximation/screened.png) | bin | 7338 -> 7338 bytes | |||
| -rw-r--r-- | source/know/concept/random-phase-approximation/pairbubble.avif | bin | 0 -> 3558 bytes | |||
| -rw-r--r-- | source/know/concept/random-phase-approximation/self-energy.avif | bin | 0 -> 7165 bytes | |||
| -rw-r--r-- | source/know/concept/random-phase-approximation/self-energy.png (renamed from source/know/concept/random-phase-approximation/rpasigma.png) | bin | 10310 -> 10310 bytes |
7 files changed, 4 insertions, 12 deletions
diff --git a/source/know/concept/random-phase-approximation/dyson.avif b/source/know/concept/random-phase-approximation/dyson.avif Binary files differnew file mode 100644 index 0000000..dc80856 --- /dev/null +++ b/source/know/concept/random-phase-approximation/dyson.avif 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: -<a href="rpasigma.png"> -<img src="rpasigma.png" style="width:92%"> -</a> +{% 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: -<a href="screened.png"> -<img src="screened.png" style="width:95%"> -</a> +{% 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/): -<a href="dyson.png"> -<img src="dyson.png" style="width:55%"> -</a> +{% 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 $$\tilde{\vb{q}} \equiv (\vb{q}, i \omega_n^F)$$: -<a href="pairbubble.png"> -<img src="pairbubble.png" style="width:45%"> -</a> +{% 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 Binary files differnew file mode 100644 index 0000000..f3f6cbe --- /dev/null +++ b/source/know/concept/random-phase-approximation/interaction.avif diff --git a/source/know/concept/random-phase-approximation/screened.png b/source/know/concept/random-phase-approximation/interaction.png Binary files differindex bb5ccdd..bb5ccdd 100644 --- a/source/know/concept/random-phase-approximation/screened.png +++ b/source/know/concept/random-phase-approximation/interaction.png diff --git a/source/know/concept/random-phase-approximation/pairbubble.avif b/source/know/concept/random-phase-approximation/pairbubble.avif Binary files differnew file mode 100644 index 0000000..bca964e --- /dev/null +++ b/source/know/concept/random-phase-approximation/pairbubble.avif diff --git a/source/know/concept/random-phase-approximation/self-energy.avif b/source/know/concept/random-phase-approximation/self-energy.avif Binary files differnew file mode 100644 index 0000000..3ddfed7 --- /dev/null +++ b/source/know/concept/random-phase-approximation/self-energy.avif diff --git a/source/know/concept/random-phase-approximation/rpasigma.png b/source/know/concept/random-phase-approximation/self-energy.png Binary files differindex fedc9f5..fedc9f5 100644 --- a/source/know/concept/random-phase-approximation/rpasigma.png +++ b/source/know/concept/random-phase-approximation/self-energy.png |
