Tracking-of-selected-states.md

 **VERSION>=2021.09.18**
 
 # Tracking the states
-W-SLDA Toolkit allows to track observables arsing from selected states in time. Presently following quantities can be tracked:
+W-SLDA Toolkit allows to track observables arising from selected states in time. Presently 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`:  
@@ -17,10 +17,22 @@ subsetMinEn             0.0     # in eF units, deafault=0.0
 subsetMaxEn             0.0     # in eF units, deafault=0.0
 ```
 
-In the case of spin-imbalanced systems, it is also convenient to introduce a shift of quasiparticle energies when selecting the states: $`E_n \rightarrow E_n+\frac{\mu_{\uparrow}-\mu_{\downarrow}}{2}`$. This can be done automatically via enabling 
+In the case of spin-imbalanced systems, it is also convenient to introduce a shift of quasiparticle energies when selecting the states: $`E_n \rightarrow E_n+\frac{\mu_{\uparrow}-\mu_{\downarrow}}{2}`$. This can be done automatically by enabling 
 ```bash
 subsetShiftDmu          1       # if 1 then apply extra shift of quasiparticle energies by (mu_a-mu_b)/2, default=0
 ```
 
 # Example
-TODO: Andrea
+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
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+
+```bash
+# ---------------- SUBSET TRACKING ------------------
+# See: Wiki -> Tracking of selected states
+# observables (densities, currents) arising from state in the energy interval En in [subsetMinEn,subsetMaxEn]
+# will be computed, if  subsetMinEn=subsetMaxEn=0  the functionality is disables
+subsetMinEn             -0.35     # in eF units, deafault=0.0
+subsetMaxEn             0.35     # in eF units, deafault=0.0
+subsetShiftDmu          1       # if 1 then apply extra shift of quasiparticle energies by (mu_a-mu_b)/2, default=0
+```
+For the unitary Fermi Gas $`\Delta/\varepsilon_{F}=0.5`$, thus as the subset we select only in-gap states, which in this case corresponds to Andreev vortex states. They are localized in the vortex core. It is visualized below: the left half shows $`\Delta(r)/\varepsilon_{F}`$, while the right half shows `subset_rho_a`.
+![subset](uploads/448524d11f75bbd5e63179d7ba7722b9/subset.png)
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