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update docs
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LittleBug committed May 25, 2023
1 parent 9d6f900 commit e1235c2
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2 changes: 1 addition & 1 deletion docs/src/manual/ladder_3D.md
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Expand Up @@ -14,7 +14,7 @@ Define ``\vec{k}+\vec{p}=-\vec{p}' `` for the first term, then rename it as ``\v
\begin{split}
=& \int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{f\left(\frac{p^2}{2 m}-\mu\right)-f\left(-\frac{p^2}{2 m}+\mu\right)}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} \\
=& \int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{2f\left(\frac{p^2}{2 m}-\mu\right)-1}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} \\
=& -\int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{1}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} +\int \frac{d^3 \vec{p}}{(2 \pi)^3} \frac{2f\left(\frac{p^2}{2 m}-\mu\right)}{i \Omega_n-\frac{p^2}{2 m}-\frac{\left(\vec{p}+k^2\right)}{2 m}+2 \mu}
=& -\int \frac{d^3 \vec{p}}{\left(2\pi^3\right)} \frac{1}{i \Omega_n-\frac{p^2}{2 m}-\frac{(\vec{p}+\vec{k})^2}{2 m}+2 \mu} +\int \frac{d^3 \vec{p}}{(2 \pi)^3} \frac{2f\left(\frac{p^2}{2 m}-\mu\right)}{i \Omega_n-\frac{p^2}{2 m}-\frac{\left(\vec{p}+\vec{k}\right)^2}{2 m}+2 \mu}
\end{split}
```

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2 changes: 0 additions & 2 deletions src/polarization.jl
Original file line number Diff line number Diff line change
Expand Up @@ -119,7 +119,6 @@ where we subtract the UV divergent term that is a constant proportional to the U
- q: momentum
- n: matsubara frequency given in integer s.t. Ωn=2πTn
- param: other system parameters
- maxk: optional, upper limit of integral -> maxk*kF
- scaleN: optional, N of Log grid in LogDensedGrid, check CompositeGrids for more detail
- minterval: optional, actual minterval of grid is this value times min(q,kF)
- gaussN: optional, N of GaussLegendre grid in LogDensedGrid.
Expand Down Expand Up @@ -221,7 +220,6 @@ where we subtract the UV divergent term that is a constant proportional to the U
- q: momentum
- n: matsubara frequency given in integer s.t. Ωn=2πTn
- param: other system parameters
- maxk: optional, upper limit of integral -> maxk*kF
- scaleN: optional, N of Log grid in LogDensedGrid, check CompositeGrids for more detail
- minterval: optional, actual minterval of grid is this value times min(q,kF)
- gaussN: optional, N of GaussLegendre grid in LogDensedGrid.
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