Dear Sudin, The resonances do not correspond necessarily to the eigenvalues of the central system. You can see it this way: since the partition system-leads is arbitrary, someone can include some sites of the leads in the system, and therefore, he gets more eigenvalues. This will not give him more resonances because the profile of the conductance remains unchanged by this operation. For your case, the model can be solved analytically. You can notice that for very small tc, the resonances are obtained when sin(N *k) ~sin(k). k being the momentum and N the number of sites. This is situation corresponds to the case of G_1N =G_11=G_NN, where G_ij is the Green's function between the site i and j of a chain of length N (non-attached chain). {G_11=sin(N k)/sin((N+1)k) and G_1N= sin (k)/sin((N+1)k). } If you add the plot of sin(N k) and sin(k) to your transmission plot, you will notice that. (This is true for tc <<1). I hope this helps Abbout Adel On Tue, Jan 23, 2018 at 7:53 AM, SUDIN GANGULY wrote:

Dear Sir,

Recently I was doing a problem on a 1D chain. The problem I faced is as follows.

For a 1D chain, suppose I have taken 5 sites and set the hopping strength between lead and system very small compared to the system hopping. Now since we have 5 sites, from the Hamiltonian of the system we'll have 5 eigenvalues and if we calculate the transmission coefficient we shall have 5 peaks each occurs at particular eigenvalue.

But in my case, I am getting only three peaks. Am I missing something here? Please help me. The following code I have used for the transmission calculation.

#===================CODE================== import kwant # For plotting from matplotlib import pyplot import numpy as np

def make_system(a=1, t=1.0, L=5): # Start with an empty tight-binding system and a single square lattice. # `a` is the lattice constant (by default set to 1 for simplicity.

lat = kwant.lattice.chain(a)

syst = kwant.Builder()

#### Define the scattering region. #### for x in range (L): syst[(lat(x))] = 0

#syst[(lat(x) for x in range(L))] = onsite syst[lat.neighbors()] = -t

#### Define and attach the leads. #### lead = kwant.Builder(kwant.TranslationalSymmetry([-a])) lead[(lat(0))] = 0 lead[lat.neighbors()] = -t

syst.attach_lead(lead) syst.attach_lead(lead.reversed())

#============== set hopping between lead and system ============ for i in syst.leads[0].interface: for j in syst.neighbors(i): syst[i,j] = 0.1

for i in syst.leads[1].interface: for j in syst.neighbors(i): syst[i,j] = 0.1

return syst #================================================================ def main(): syst = make_system()

# Check that the system looks as intended. kwant.plot(syst)

# Finalize the system. syst = syst.finalized()

Es = np.linspace(-1.99, 1.99, 800)

data = [] totdos = [] for e in Es: smatrix = kwant.smatrix(syst, e) T = smatrix.transmission(1, 0) ldos = kwant.ldos(syst, e) totdos.append(sum(ldos)/len(ldos)) data.append(T)

print ('%0.3f' % e, '%.4f' % T, sum(ldos)/len(ldos))

pyplot.figure() pyplot.plot(Es, data) pyplot.xlabel("energy [t]") pyplot.ylabel("conductance [e^2/h]") pyplot.show()

# Call the main function if the script gets executed (as opposed to imported). # See http://docs.python.org/library/__main__.html. if __name__ == '__main__': main()

#================End CODE======================= -- সুদিন

-- Abbout Adel