ASLDA - asymmetric superfluid local density approximation

The functional has the generic form:

\begin{aligned}
\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots) & =  \alpha_{\uparrow}(n_{\uparrow},n_{\downarrow})\frac{\tau_{\uparrow}}{2} + 
    \alpha_{\downarrow}(n_{\uparrow},n_{\downarrow})\frac{\tau_{\downarrow}}{2} \\
&+
    D(n_{\uparrow},n_{\downarrow})
    +
    g(n_{\uparrow},n_{\downarrow})\nu^{\dagger}\nu \\ 
    &+ [1-\alpha_{\uparrow}(n_{\uparrow},n_{\downarrow})]\dfrac{\bm{j}_{\uparrow}^2}{2n_{\uparrow}}
    + [1-\alpha_{\downarrow}(n_{\uparrow},n_{\downarrow})]\dfrac{\bm{j}_{\downarrow}^2}{2n_{\downarrow}}
\end{aligned}

TODO