Functionals.md

+The functional must be selected at compilation stage in *predefines.h* file:  
+```c
+/**
+ * Select functional:
+ *  - SLDA: 
+ *      for simulating unitary Fermi gas, 
+ *      it sets effective mass of particles to 1.0 which assures better convergence properties,
+ *      in case of time time-dependent calculations SLDA is about 2x faster than ASLDA.
+ *  - ASLDA:
+ *      for simulating unitary Fermi gas,
+ *      at qualitative level it produces results compatible with SLDA, however it is more accurate,
+ *      due to presence of current terms in the functional it has worse convergence properties.
+ *  - BDG:
+ *      for simulating systems in BCS regime,
+ *      equations of motion are equivalent to Bogoliubov-de-Gennes equations,
+ *      you MUST set aBdG value in input file when using this functional.
+ * */
+// #define FUNCTIONAL SLDA
+#define FUNCTIONAL ASLDA
+// #define FUNCTIONAL BDG
+```
+
 # ASLDA - asymmetric superfluid local density approximation
-The functional has the generic form:
+The ASLDA functional has been designed in order to capture properties of **strongly interacting unitary Fermi gas**. The functional has the generic form:
 ```math
 \begin{aligned}
 \mathcal{E}_{\textrm{edf}}(n,\nu,\ldots) & =  \alpha_{\uparrow}(n_{\uparrow},n_{\downarrow})\frac{\tau_{\uparrow}}{2} + 
@@ -62,3 +84,13 @@ The term in ASLDA functional that depends on the currents $`\bm{j}_{\sigma}`$ in
 
 Below we provide plot showing relative energy change (in %) between simulations of SLDA and ASLDA that compute the energy of N fermions (both even and odd particle numbers) in the spin-symmetric unitary Fermi gas trapped in an isotropic harmonic oscillator.  For more info see [supplemental material of this paper](https://arxiv.org/abs/1306.4266).  
 ![slda_vs_aslda](uploads/073efe244d1ab67bed1314af5cf0fc21/slda_vs_aslda.png)
+
+# BdG - Bogoliubov de-Gennes functional
+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:
+```math
+\mathcal{E}_{\textrm{edf}}(n,\nu,\ldots)  =  \frac{\tau_{\uparrow}}{2} + 
+    \frac{\tau_{\downarrow}}{2} 
+    + g\nu^{\dagger}\nu 
+```  
+The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m`$. 
+ 
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