Questions and Answers: Closed Question
Status: Closed
Anonymous @ 08:03 PM on 11 Jun, 2007
Time-dependent NEGF
In the time-dependent NEGF equation, given a sigma_in(t,t’) due to the dot, I am getting
an I-V equation that is making it difficult for me to group terms. For instance, looking at the analogue of the first term of I = 2q/hbar. int dE TrGin I get I1 = q/ihbar. int dt1 TrSigma_in.G^dagger-G.Sigma_in
Now, because of the different order of the time arguments in the G and G^dagger terms, I cannot pool these to write it as a spectral function A = i(G-G^dagger). Similarly, I can’t seem to take Sigma – Sigma^dagger to get Gamma. Is this correct?
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Supriyo Datta @ 08:06 PM on 11 Jun, 2007
I think I(t,t) should be real except for numerical errors ..We can write
I_L(t,t) = (1/i/hbar) int dt1 TraceSigin_LG+-GSigin_L
= (1/i/hbar) int dt1 sum(i,j) Sigin_L (i,j;t,t1) G+(j,i;t1,t) – G(i,j;t,t1) sigin_L+(j,i;t1,t) = (1/i/hbar) int dt1 sum(i,j) Sigin_L (i,j;t,t1) G(i,j;t,t1)* – G(i,j;t,t1) sigin_L(i,j;t,t1)* =(1/i) * (X – X*) = Real.
In the first step I made use of sigin_L = sigin_L+ and in the second step I made use of A+(i,j;t,t1) = A(j,i;t1,t)*
Makes sense?
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