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次へ: total charge from contour 上へ: in the equilibrium 戻る: in the equilibrium

total charge from the retarded Green function

total charge, $n_{tot}$, is calculated from the retarded Green function
$\displaystyle A_{ij}(\omega )$ $\textstyle =$ $\displaystyle -\frac{1}{\pi} {\rm Im} G_{ij}^{R}(w)$ (73)
$\displaystyle \rho_{ij}$ $\textstyle =$ $\displaystyle \int^{\mu} d\omega A_{ij}(w)$ (74)
  $\textstyle =$ $\displaystyle -\frac{1}{\pi} {\rm Im} \int^{\mu} d\omega G_{ij}^{R}(w)$ (75)
$\displaystyle n_{tot}$ $\textstyle =$ $\displaystyle {\rm Tr}[ \rho ]$ (76)

where $G^R(\omega ) = G(\omega +i\delta )$



kino 平成18年4月17日