Dear all, I have two simple questions concerning electronic transport with spins with no interaction: If I take the program spin_orbit.py from the tutorial and call the system sys=make_system ( alpha=0, ez=0, W=2, L=2) # no spin orbit interaction print matrix.round(kwant.smatrix(sys,energy=1.7).data , 2 ) I choose the energy E=1.7 because one mode is closed. the result is: [[-0.00-0.j 0.00-0.j 0.41+0.43j -0.74-0.33j] [ 0.00-0.j -0.00-0.j -0.80+0.08j -0.52+0.28j] [ 0.41+0.43j -0.74-0.33j -0.00-0.j 0.00-0.j ] [-0.80+0.08j -0.52+0.28j 0.00-0.j -0.00-0.j ]] What surprises me is that there is scattering between spins knowing that the Hamiltonians for the two spins are separated without interaction ! This seems to appear only when one mode is closed. To understand better and check this result, I rewrote the program using two lattices (as for electrons and holes). the program is attached with the Email. The result for the scattering matrix is [[ 0.00-0.j -0.16+0.99j 0.00+0.j 0.00+0.j ] [-0.16+0.99j 0.00+0.j 0.00+0.j 0.00+0.j ] [ 0.00+0.j 0.00+0.j 0.00+0.j -0.16+0.99j] [ 0.00+0.j 0.00+0.j -0.16+0.99j 0.00+0.j ]] The result is now better because there is no scattering between spins. My Question is :what am I missing? The second question concerns the position of the coefficients in the scattering matrix. We have the Hamiltonian [image: H=h \otimes 1_{2\times2}] where [image: \otimes] is the Kronecker product and [image: h] the spinlessHamiltonian. The scattering matrix is given by : [image: S=-1+2\pi i W^\dagger \frac{1}{E-H-\Sigma} W] [image: W] is the coupling matrix and [image: \Sigma] the self energy If we look at the simple system [image: ( L=2,W=2)] all the matrices are square and we can easily proove, just by the properties of the Kronecker poduct that the scattering matrix can be written as: [image: S=s\otimes 1_{2\times2}] Where [image: s] is the scattering matrix without spin. [image: s= \left(\begin{array} {c c} r & t \\ t^\prime & r^\prime \end{array}\right)] [image: t] is the transmission matrix. So I am expecting a scattering matrix with the followin form: [image: S= \left(\begin{array} {c c c c} r &0 & t & 0 \\ 0 &r & 0 & t \\ t^\prime &0 & r^\prime & 0 \\ 0& t^\prime & 0 & r^\prime \end{array}\right)] This is consistent with the result with two lattices but still the position of the coefficients are different from the one obtained from the Hamiltonian base. So I suggest that you are using different base. The question I ask is: in order to know the position of coefficients corresponding to different modes or different spins, which formula do you use to obtain the scattering matrix. is it a matrix inversion or some recursive method ? Thank you in advance. Regards, A. Abbout