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  • Chemical potentials control

Chemical potentials control · Changes

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Update Chemical potentials control authored Feb 21, 2022 by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Chemical-potentials-control.md
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# Ajusting of chemical potentials
Static codes adjust chemical potentials automatically in such a way to provide a solution with requested particle number. Following parameters control adjusting process:
```bash
muchange 0.5 # coefficient for changing chemical potential, default=0.5
mumaxchange 0.05 # maximal allowed changed of chemical potential per iteration,
# in units of Fermi energy
muchange 0.5 # coefficient for changing chemical potential, default=0.5, for both components
# muchange_a 0.5 # or you can control muchange for each component separately using tags with `a` ...
# muchange_b 0.5 # ... and `b` suffixes.
mumaxchange 0.05 # maximal amount that chemical potential can change between iterations, in units of Fermi energy
# mumaxchange_a 0.05 # or you can control mumaxchange for each component separately using tags with `a` ...
# mumaxchange_b 0.05 # ... and `b` suffixes.
```
Chemical potentials are adjusted according to rule:
```math
\begin{aligned}
\Delta\mu_{\sigma}^{(i)} &= \textrm{muchange}\,\frac{N_{\sigma}^{(\textrm{req.})}-N_{\sigma}^{(i)}}{N_{\sigma}^{(\textrm{req.})}}\\
\textrm{if}\,|\Delta\mu_{\sigma}^{(i)}/\varepsilon_F|&>\textrm{mumaxchange}:\,\textrm{decrease}\,\textrm{magnitude}\,\textrm{of}\,\Delta\mu_{\sigma}^{(i)}\\
\Delta\mu_{\sigma}^{(i)} &= \textrm{muchange}_{\sigma}\,\frac{N_{\sigma}^{(\textrm{req.})}-N_{\sigma}^{(i)}}{N_{\sigma}^{(\textrm{req.})}}\\
\textrm{if}\,|\Delta\mu_{\sigma}^{(i)}/\varepsilon_F|&>\textrm{mumaxchange}_{\sigma}:\,\textrm{decrease}\,\textrm{magnitude}\,\textrm{of}\,\Delta\mu_{\sigma}^{(i)}\\
\mu_{\sigma}^{(i+1)} &= \mu_{\sigma}^{(i+1)} + \Delta\mu_{\sigma}^{(i)}
\end{aligned}
```
......
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