Dear Amrit,

You wrote:

" this is based on Eq. 25 in energy domain of https://arxiv.org/pdf/1307.6419.pdf "

and deduced that G^r(E) = -i*\Psi(E)*\Psi^\dag(E).

Your deduction must be wrong. I suggest to you to do the calculation for a simple case and test your formula in a clean 1D system.
G^r=1/(EE-H+i eta) ==> G^r_ij= Sum_k Psi_ik 1/(EF-E_k+i eta) Psi_kj

The sum over k can be changed to a an integral over energy

G^r_ij= Integral Psi_i(E) 1/(EF-E_k+i eta) Psi_j(E)^dagger * dk/dE *dE

when you carry on the calculation,you see that there is a term which is missing in your formula which is dk/dE. This term is the inverse of the velocity. If you carry the calculation for the 1D case, you will find the correct form known in literature.

I want to bring to your attention that for Greens energy calculation, the evanescent modes are also taken into account and not only the propagating ones (the one obtained by kwant. wavefuntion are propagating) .

I hope this helps,

Regards,

Adel

On Sat, Sep 14, 2019 at 9:59 PM Amrit Poudel <quantum.apg@gmail.com> wrote:

Hello Kwant users,

I am trying to compare the retarded Green's function of a simple 1D wire attached to two leads using two different methods:

(I) Using scattering wave function obtained from the Kwant software and using Eq. 25 in energy domain of "Numerical simulations of time resolved quantum electronics (https://arxiv.org/abs/1307.6419) written by Kwant authors.

(II) Direct computation of the retarded Green's function by inverting device Hamiltonian with self energies of the attached leads (again computed from the Kwant software): G^r(E) = [E+\i*\eta - H- \Sigma^r_{leads}]^{-1} for a relatively small system size (5 sites in the attached example). Here both H and \Sigma^r are computed from the Kwant software.

However, I find that these two results do not agree even in a simple 1D example when on-site potential is present in the few sites of device or scattering region only.

I have attached the Python script with this email.

Does anyone know the reason behind the discrepancy between the two methods?I would greatly appreciate any comments/suggestions on how we can resolve this error?

Thanks!