# Is this a correct integral for calculating current of the given Green's function?

I am trying to calculate numerically a current from the given Green's function. I am aware that to calculate density of states of a Green's function I must do the integral as follows:

$\tag1\ DOS(E) =\frac{ -1 }{2*\pi^2}*Im*\int_{-\pi}^{\pi}G(E,k)*dk$

and,

$\tag2\ G(E) =\frac{ 1 }{E-i*n-2*cos(k)}$

is a Green's advanced function. Equation (1) and (2) shows how to calculated DOS using the integral. To calculate current for simple two contacts model of quantum transport I assume the following equation:

$\tag3\ I(V) =\frac{ 2*e }{h}*Re\int_{-\infty}^{\infty}T(E)*(F(E-V)-F(E))*dE$

and T(E) is the transmitance function expressed in terms of Gamma's and Retarded/Advanced Green's function. My question is that in order to calculate current numerically do I have to do one integral over dE and keeping k constant at some value or do I have to do double integral (first one over dk and second integral over dE)? Both give me same results in curve plot (I-V line going through (0,0) but amplitudes are different)

$\tag4\ I(V) =\frac{ 2*e }{h}*Re\int_{-\infty}^{\infty}T(E)*(F(E-V)-F(E))*dE, and: k-constant$

$\tag5\ I(V) =\frac{ 2*e }{h}*Re\int_{-\infty}^{\infty}*(\int_{-\pi}^{\pi}T(E)*(F(E-V)-F(E))*dk)*dE$

• I'm not used to see such codings on this website, perhaps could you present your question with the physical concepts instead of a code? Jul 7, 2017 at 21:11
• @gingras.ol, Thanks for reply. I removed the code and added physical concepts as you suggested. Jul 8, 2017 at 16:06