... | ... | @@ -54,9 +54,9 @@ $`\tau_{\uparrow}(r) = \sum_{|E_n|<E_c}|\nabla u_{n,\uparrow}(r)|^2 f_{\beta}(E_ |
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* `tau_b`:
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$`\tau_{\downarrow}(r) = \sum_{|E_n|<E_c}|\nabla v_{n,\downarrow}(r)|^2 f_{\beta}(-E_n)`$
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* `j_a_x`, `j_a_y`, `j_a_z`:
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$`\vec{j}_{\uparrow}(r) = -\sum_{|E_n|<E_c} \textrm{Im}[u_{n,\uparrow}(r)\nabla u_{n,\uparrow}^*(r)]`$
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$`\vec{j}_{\uparrow}(r) = -\sum_{|E_n|<E_c} \textrm{Im}[u_{n,\uparrow}(r)\nabla u_{n,\uparrow}^*(r)]f_{\beta}(E_n)`$
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* `j_b_x`, `j_b_y`, `j_b_z`:
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$`\vec{j}_{\downarrow}(r) = \sum_{|E_n|<E_c} \textrm{Im}[v_{n,\downarrow}(r)\nabla v_{n,\downarrow}^*(r)]`$
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$`\vec{j}_{\downarrow}(r) = \sum_{|E_n|<E_c} \textrm{Im}[v_{n,\downarrow}(r)\nabla v_{n,\downarrow}^*(r)]f_{\beta}(-E_n)`$
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In these formulas $`E_{n}`$ denotes quasi-particle energy and $`E_c`$ is energy cut-off scale. Fermi distribution function $`f_{\beta}(E)=1/(\exp(\beta E)+1)`$ is introduced to model temperature $`T=1/\beta`$ effects.
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