| ... | @@ -86,7 +86,7 @@ Below we provide plot showing relative energy change (in %) between simulations |
... | @@ -86,7 +86,7 @@ Below we provide plot showing relative energy change (in %) between simulations |
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# BdG - Bogoliubov de-Gennes functional
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# BdG - Bogoliubov de-Gennes functional
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The BdG functional is equivalent to Bogoliubov de-Gennes mean-field approximation. This approximation is valid in BCS regime, under assumption $`-ak_F`<1$. The functional has form:
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The BdG functional is equivalent to Bogoliubov de-Gennes mean-field approximation. This approximation is valid in BCS regime, under assumption $`-ak_F<1`$. The functional has form:
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```math
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```math
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\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots) = \frac{\tau_{\uparrow}}{2} +
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\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots) = \frac{\tau_{\uparrow}}{2} +
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\frac{\tau_{\downarrow}}{2}
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\frac{\tau_{\downarrow}}{2}
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| ... | @@ -94,7 +94,7 @@ The BdG functional is equivalent to Bogoliubov de-Gennes mean-field approximati |
... | @@ -94,7 +94,7 @@ The BdG functional is equivalent to Bogoliubov de-Gennes mean-field approximati |
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```
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```
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The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m`$.
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The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m`$.
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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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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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