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author | Prefetch | 2023-01-01 16:40:56 +0100 |
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committer | Prefetch | 2023-01-01 17:02:29 +0100 |
commit | b1a9b1b9b2f04efd6dc39bd2a02c544d34d1259c (patch) | |
tree | 1fd87919deee17e58f8ad19c09abd54bd4a70886 /source/know/concept/random-phase-approximation/index.md | |
parent | 1d700ab734aa9b6711eb31796beb25cb7659d8e0 (diff) |
Change license, add Makefile, add image caching control
Diffstat (limited to 'source/know/concept/random-phase-approximation/index.md')
-rw-r--r-- | source/know/concept/random-phase-approximation/index.md | 12 |
1 files changed, 8 insertions, 4 deletions
diff --git a/source/know/concept/random-phase-approximation/index.md b/source/know/concept/random-phase-approximation/index.md index 0d0b428..03fd302 100644 --- a/source/know/concept/random-phase-approximation/index.md +++ b/source/know/concept/random-phase-approximation/index.md @@ -71,17 +71,20 @@ 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" %} +{% 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" %} +{% 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" %} +{% 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: @@ -98,7 +101,8 @@ 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" %} +{% 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: |