Tracking-of-selected-states.md

 **VERSION>=2021.09.18**
 
 # Tracking the states
-W-SLDA Toolkit allows to track observables arising from selected states in time. Presently following quantities can be tracked:
+W-SLDA Toolkit allows the tracking of observables arising from selected states in time. Presently, the following quantities can be tracked:
 * `subset_rho_a`:  
 $`n_{\uparrow}^{\textrm{(subset)}}(r)= \sum_{E_{\textrm{min}}^{\textrm{(subset)}}<E_n<E_{\textrm{max}}^{\textrm{(subset)}}}|u_{n,\uparrow}(r)|^2 f_{\beta}(E_n)`$
 * `subset_rho_b`:  
@@ -21,6 +21,8 @@ In the case of spin-imbalanced systems, it is also convenient to introduce a shi
 ```bash
 subsetShiftDmu          1       # if 1 then apply extra shift of quasiparticle energies by (mu_a-mu_b)/2, default=0
 ```
+# Limitations
+The states to be tracked and contracted into `subset_rho` and `subset_j` are tagged at the beginning of the simulations. It means that we select states based on their energies at `t=0`. However, as the dynamics proceed energies of the states can change as well, so some of them can acquire energy that is out of the given range, and some that were not included initially can acquire energy within the considered energy range. These effects are not taken into account by the presented prescription. 
 
 # Example
 Below we present a snapshot from a simulation with SLDA functional for the spin-symmetric system. `td-wslda-2d` has been used. The unitary Fermi gas is confined in a tube, and the vortex dipole is imprinted in the initial state. Following options for subset tracking were used