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update README with NEGF equations
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liborsold committed Apr 13, 2024
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Expand Up @@ -25,21 +25,25 @@ The complete description and calculation are provided in the ```examples/one-dim
## NEGF Equations

The *retarded Green's function*

$$
\mathbf{G}^{\mathrm{R}}=[E \mathbf{I}-\mathbf{H}-\mathbf{\Sigma}]^{-1}
$$

along with the *advanced Green's function*

$$
\mathbf{G}^{\mathrm{A}} = \left[ \mathbf{G}^{\mathrm{R}} \right]^\dagger
$$

provide the *spectral function*

$$
\mathbf{A}=i\left[\mathbf{G}^{\mathrm{R}}-\mathbf{G}^{\mathrm{A}}\right]
$$

and are used to solve for the *"electron occupation" Green's function* ($\mathbf{G}^{\mathrm{n}} \equiv -i \mathbf{G}^< $)

$$
\mathbf{G}^{\mathrm{n}}=\mathbf{G}^{\mathrm{R}} \Sigma^{\mathrm{in}} \mathbf{G}^{\mathrm{A}}
$$
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