Functionals.md

+[[_TOC_]]
+
+# Selecting the functional
 The functional must be selected at compilation stage in *predefines.h* file:  
 ```c
 /**
@@ -92,9 +95,15 @@ 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 $`g=4\pi\hbar^2a/m`$.  
+The (bare) coupling constant $`g`$ is related to scattering length by the formula $`g=4\pi\hbar^2a/m_r`$, where $`m_r`$ is reduced mass.  
 
 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)  
  
+# Regularization scheme of pairing field
+By default, W-SLDA implements a regularization scheme of the pairing field known as Superfluid Local Density Approximation (SLDA). Precisely, the implemented formulas are (9.86)-(9.87) from paper [arXiv:1008.3933](https://arxiv.org/abs/1008.3933).  
+
+*Note 1*: The regularization scheme is only valid for 3D systems. If you want to execute pure 2D or 1D calculations, you need to provide your regularization procedure. For more info see [Strict 2D or 1D modes](Strict 2D or 1D mode).  
+
+*Note 2*: The regularization uses average effective mass $`\alpha_{+}`$ and average chemical potential $`\mu_{+}`$. Thus, the regularization is valid for spin-imbalanced and mass-imbalanced systems as well.