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Functionals · Changes

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Update Functionals authored Dec 13, 2020 by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Functionals.md
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......@@ -92,5 +92,9 @@ The BdG functional is equivalent to Bogoliubov de-Gennes mean-field approximati
\frac{\tau_{\downarrow}}{2}
+ g\nu^{\dagger}\nu
```
The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m`$.
\ No newline at end of file
The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m`$.
Below we provide predictions of BdG functional for total energy and paring gap as a function of coupling constant $`-ak_F`$ computed for uniform and spin-symmetric system. Results are compared with predictions of BCS theory, and as expected the agreement is observed for $`-ak_F`<1$.
![BdG-E](uploads/a3e8e87c80efd2c4a31d2ea50dec6191/BdG-E.png)
![BdG-D](uploads/7529bf3d47e71594ef42d2b2b3a51865/BdG-D.png)
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