Dear Joe, Thanks a lot for clarifying these points for me. So the local densities and local currents in Tutorial 2.7 correspond to the scattering state incoming in mode 0 of lead 0. I still feel confused. Why we only consider a *single* scattering state from one lead? Can the local densities and currents associated with a *single* scattering state show the transport properties of the system? Could you give me some reference papers for local densities and currents? Best wishes, Hosein Khani
On Tue, Jul 4, 2017 at 4:17 PM, Joseph Weston <joseph.westo...@gmail.com> wrote: > HI Hosein, > > > > I want to use kwant to calculate the local densities and currents, but > > I do not understand some of the code lines. For the local density of > > states, we can obtain it from: > > wf = kwant.wave_function(sys, energy) > > LDOS=((abs(wf(0))**2).sum(axis=0)+(abs(wf(1))**2).sum(axis=0))/(pi*2.) > > > here wf(0) and wf(1) is the wavefunction for the left and right leads > > of a two terminal system. > > No. 'wf(0)' is a *sequence of wavefunctions of scattering states*, each > one defined over the scattering region (the system to which you attached > the leads). Each of the scattering wavefunctions is associated with a > single incoming mode from lead 0. 'wf(1)' is the same quantity, but > referring to the incoming modes from lead 1. > > > In Tutorial 2.7, we use > > wf = kwant.wave_function(syst, energy=-1, params=params) > > psi = wf(0)[0] > > Here wf(0)[0] includes all the leads and modes? > > No. As we saw in my previous response 'wf(0)' is a sequence of > scattering wavefunctions. 'wf(0)[0]' is therefore the first wavefunction > in this sequence, which corresponds to the scattering state incoming in > mode 0 of lead 0. > > > > In Tutorial 2.7, we use the following lines to calculate the local > > density: > > up, down = psi[::2], psi[1::2] > > density = np.abs(up)**2 + np.abs(down)**2 > > rho = kwant.operator.Density(syst) > > density = rho(psi) > > > > Will the two density give the same results as LDOS? > > No; the "density" being referred to above is one associated with a > *single* scattering state. > The LDOS that Kwant defines is the sum of the densities of all the > scattering states (at a given energy). > > > Happy Kwanting, > > Joe > > >
