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Update Regularization schemes of the pairing field authored by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Regularization-schemes-of-the-pairing-field.md
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...@@ -64,4 +64,8 @@ In practical applications, we observe that the energy when applied the spherical ...@@ -64,4 +64,8 @@ In practical applications, we observe that the energy when applied the spherical
![wiki2](uploads/3c18f9d061adcea98d658125b498a1ad/wiki2.png) ![wiki2](uploads/3c18f9d061adcea98d658125b498a1ad/wiki2.png)
It is clearly visible, that for evolution with the cubic cutoff the energy is conserved up to high accuracy, while for spherical cutoff the quality of the energy conservation is significantly lower. It is clearly visible, that for evolution with the cubic cutoff the energy is conserved up to high accuracy, while for spherical cutoff the quality of the energy conservation is significantly lower.
`wlog` files for these runs:
* [cubic.wlog](uploads/5aff56cbbd8ee97046cc1c3d10a49867/cubic.wlog)
* [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. 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.
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