Many-Body I - TDDFT.org
Many-Body I - TDDFT.org
Many-Body I - TDDFT.org
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The GW Approximation<br />
Σ ( x , x';<br />
ω)<br />
i<br />
= ∫ W ( x,<br />
x';<br />
ω')<br />
G ( x,<br />
x';<br />
ω + ω')<br />
e<br />
2π<br />
where x ≡ ( r,<br />
ξ ) is space+spin<br />
iδω ' d<br />
ω'<br />
In the time domain<br />
Σ( x , x';<br />
t − t')<br />
= iW ( x,<br />
x';<br />
t − t')<br />
G(<br />
x,<br />
x';<br />
t − t')<br />
W is the dynamically screened Coulomb interaction between electrons<br />
<strong>Many</strong>-body theory and <strong>TDDFT</strong> - Benasque, 30/31 Aug 2006 18