Regularization-schemes-of-the-pairing-field.md

@@ -70,3 +70,22 @@ It is clearly visible, that for evolution with the cubic cutoff the energy is co
 * [spherical.wlog](uploads/e642fe76e9496d2305f4c462ebc61e72/spherical.wlog)
 
 In conclusion, we find that typically for trajectories of length $`te_F\approx1000`$ the spherical cutoff provides reasonable accuracy, while for generation of long trajectories $`te_F\gg 1000`$ it is recommended to use the cubic cutoff. 
+
+# Known issues
+Below we present results for the uniform unitary Fermi gas as a function of lattice spacing, while keeping the fixed volume of the box. Note that the lattice spacing defines value of the energy cut-off $`E_c\approx\frac{p_c^2}{2}=\frac{\pi^2}{2DX^2}`$. Conditions of the test are as follow:
+```
+# VOLUME: 32 x 32 x 32
+# ENERGY DENSITY FUNCTIONAL: SLDA
+# UNIFORM_TEST_MODE: Setting number of particles to be: (554.000000,554.000000)
+```
+
+The result for the total energy is:
+
+|  DX  | Spherical cut-off | Cubic cut-off |
+| -----|-------------------|---------------|
+| 1.0  | 0.39761           | 0.39926       |
+| 0.8  | 0.39834           | 0.38539       |
+| 0.5  | 0.39825           | 0.36422       |
+
+In the case of the cubic cut-off, we observe the dependence of the lattice spacing. This issue needs further investigation.  
+For raw data see: [test-spherical-vs-cubic.txt](uploads/4c97d8a36df69d5d8e1c698839e2f2ed/test-spherical-vs-cubic.txt)