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  • Finite temperature calculations

Finite temperature calculations · Changes

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Update Finite temperature calculations authored May 20, 2021 by Gabriel Wlazłowski's avatar Gabriel Wlazłowski
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Finite-temperature-calculations.md
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......@@ -5,11 +5,11 @@ Finite temperature effects are introduced by adding quasiparticle occupation pro
```math
f_{\beta}(E_n)=\dfrac{1}{\exp(\beta E_n)+1}
```
to definition of densities (see [here](https://gitlab.fizyka.pw.edu.pl/gabrielw/wslda/-/wikis/Physical%20quantities#densities) from explicit formulas). Here $`\beta=1/T`$ is inverse of temperature. In zero temperature limit this function reduced to step function. Quasiparticle energies $`E_n`$ are taken from solution of Bogoliubov-de Gennes type equations
to definition of densities (see [here](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/wikis/Physical%20quantities#densities) from explicit formulas). Here $`\beta=1/T`$ is inverse of temperature. In zero temperature limit this function reduced to step function. Quasiparticle energies $`E_n`$ are taken from solution of Bogoliubov-de Gennes type equations
```math
H_{\textrm{BdG}} \begin{pmatrix}u_{n\uparrow}(r) \\ v_{n\downarrow}(r)\end{pmatrix}= E_n\begin{pmatrix}u_{n\uparrow}(r) \\ v_{n\downarrow}(r)\end{pmatrix}
```
See [here](https://gitlab.fizyka.pw.edu.pl/gabrielw/wslda/-/wikis/Physical%20quantities#potentials) from explicit form of $`H_{\textrm{BdG}}`$.
See [here](https://gitlab.fizyka.pw.edu.pl/wtools/wslda/-/wikis/Physical%20quantities#potentials) from explicit form of $`H_{\textrm{BdG}}`$.
Presently, **definition of densities is the only place where temperature enters into calculation process**. In general finite temperature DFT allows energy density functional $`\mathcal{E}_{\textrm{edf}}`$ to be temperature dependent, which is not the case neither (A)SLDA or BdG functionals.
......
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