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# Stabilization scheme
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Some of the terms in the EDF introduce the time-dependent propagation of the high-momenta components. Examples are terms that contain division by density and may lead to noise generation in regions where density vanishes.
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Some terms in the EDF introduce time-dependent propagation of the high-momentum components. Examples are terms that involve division by density and may generate noise in regions where density vanishes.
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These modes can amplify during the time-dependent propagation and destabilize the integration scheme. To avoid this, we introduced the filtering scheme.
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1. compute mean-field $`V_\sigma(\vec{r})`$,
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2. go to Fourier space $`V_\sigma(\vec{k})`$,
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| ... | ... | @@ -11,11 +11,10 @@ As the filter function, we use the Fermi-Dirac function: |
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FD(e_k,\mu, T)=\frac{1}{\exp[\frac{e_k-\mu}{T}]+1}
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```
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The same procedure can be used to folder noise that is generated in the pairing potential $`\Delta(\vec{r})`$.
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The same procedure can be used to filter noise that is generated in the pairing potential $`\Delta(\vec{r})`$.
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# Testing script
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You can use the attached script [tools/high-frequency-filter.py](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/blob/devel/tools/high-frequency-filter.py) to test the impact of the filtering scheme on the input signal. Below is an example of the script output.
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You can use the attached script [tools/high-frequency-filter.py](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/tree/public/tools/high-frequency-filter.py) to test the impact of the filtering scheme on the input signal. See [here](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/blob/public/tools/high-frequency-filter.png) for the script output.
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# Controlling the filter
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The filter can be controlled via the input file:
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