| ... | ... | @@ -95,7 +95,7 @@ The BdG functional is equivalent to Bogoliubov de-Gennes mean-field approximati |
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\alpha_\downarrow\frac{\tau_{\downarrow}}{2}
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+ g\nu^{\dagger}\nu
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```
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The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m_r`$, where $`m_r`$ is twice of reduced mass, i.e.: $`\frac{1}{m_r}=\frac{1}{2}(\alpha_\uparrow+\alpha_\downarrow)`$.
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The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m_r`$, where $`m_r`$ is twice of reduced mass, i.e.: $`\frac{1}{m_r}=\frac{1}{2}(\alpha_\uparrow+\alpha_\downarrow)`$. Default values of effective masses are $`\alpha_\uparrow=\alpha_\downarrow=1`$. See [mass imbalanced gas in a harmonic trap](https://gitlab.fizyka.pw.edu.pl/gabrielw/wslda/-/wikis/st-wslda-examples#example-3-mass-imbalanced-gas-in-a-harmonic-trap) to learn how to modify effective masses.
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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 $`-ak_F<1`$.
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