Sending report ...Support Center
Closed Question
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 Tr[Sigma_in.A-Gamma. Gin]
I get
I1 = q/ihbar. int dt1 Tr[Sigma_in(t,t1).G^dagger(t1,t)-G(t,t1).Sigma_in(t1,t)]
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?
Tags:
Asked by Anonymous - 1 year ago - 1 response
Status: Closed 1 Good question Report abuse
Answers (1)
-
Posted on 11 June, 2007 by Supriyo Datta
+2 0 Login to vote I think I(t,t) should be real except for numerical errors ..
reply | report abuse
We can write
I_L(t,t) = (1/i/hbar) int dt1 Trace[Sigin_L(t,t1)G+(t1,t)-G(t,t1)Sigin_L(t1,t)]
= (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?