Monitoring-of-conservation-laws.md

 **VERSION>=2022.04.05**  
 
+The W-SLDA Toolkit uses conserved quantities to monitor the stability of time integration. The quantities of special interest are:
+* _Particle number_ ($`N_a+N_b`$): this quantity is conserved almost for all cases. The special case when the total particle number may not be conserved is the situation when an external pairing field is activated. 
+* _Total energy_: if there is no time-dependent external potential, the energy is conserved. 
+
+To avoid situations where the code uses computing resources for generating trajectories that are incorrect (violation of conservation laws) there is build in mechanism for monitoring conservation laws. This option is controlled by the following tags in the input file:
+```bash
+# ---------------- CONSERVATION LAWS -----------------
+# See: Wiki -> Monitoring of conservation laws
+# # -> Energy conservation monitoring
+# Econservation_start       0        # Start to monitor energy conservation from time*eF, default=1e12 (infinity)
+# Econservation_stop        10000    # Stop to monitor energy conservation at time*eF, default=1e12 (infinity)
+# Econservation_tol         0.05     # if |[E(t)-E(start_t)]/E(start_t)|>tol then the code will terminate, default=0.05
+# # -> Particle number conservation monitoring
+# Nconservation_start       0        # Start to monitor total particle number conservation from time*eF, default=0
+# Nconservation_stop        10000    # Stop to monitor total particle number conservation at time*eF, default=1e12 (infinity)
+# Nconservation_tol         0.05     # if |[N(t)-N(start_t)]/N(start_t)|>tol then the code will terminate, default=0.05
+``` 
+Note that the energy conservation checking is disabled by default while particle number conservation monitoring is activated. If the violation (measured as deviation from the initial value) is detected, the code terminates. 
+