Dear Zhang, For the hoppings method, kwant puts the hopping t_ij =t_ji* by default. So, you can not make your hamiltonian non hermitian this way. On the second hand, you can put the potential as a complex number and therefore your Hamiltonian becomes non hermitian. In this kind of situation, you may want to calculate the scattering matrix or the Green's function. To do so, you need to use the option : check_hermeticity=False. As an example, I wrote for you a small program where I have a scatterer connected to two 1D leads. in this example, I calculate the reflection coefficient R as usual. in the second part, I treat this problem in a different way where I delete the second lead and take its effect using its complex self energy as an additional potential. This way, my Hamiltonian becomes non-hermitian. A quick comparison of the result in the two methods shows that I get the same thing. I hope this helps. Regards Adel ############################### import numpy as np import kwant def make_sys(two_leads=False): def potential(site,energy,V): if two_leads: return V else: #Here we take into accont the second lead by its complex self energy self_energy=energy/2-1j*sqrt(1-(energy/2)**2) #self energy of 1D lead return V+self_energy lat = kwant.lattice.square(norbs=1) sys=kwant.Builder() sys[(lat(i,0) for i in range(1))] = potential sys[lat.neighbors()] = 1 sym=kwant.TranslationalSymmetry((0,1)) lead=kwant.Builder(sym) lead[lat(0,0)]=0 lead[lat.neighbors()]=1 sys.attach_lead(lead) if two_leads: sys.attach_lead(lead.reversed()) return sys.finalized() #system with two leads syst=make_sys(two_leads=True) kwant.plot(syst) energies=np.linspace(-1.99,0,50) Reflection1=[] for energy in energies: SM=kwant.smatrix(syst,energy=energy,in_leads=[0],out_leads=[0],params=dict(energy=energy,V=-1.8)) R=SM.transmission(0,0) Reflection1.append(R) #system with one lead and a self energy as a potential syst=make_sys(two_leads=False) kwant.plot(syst) Reflection2=[] #The Hamiltonian is non-hermitian #We use: check_hermiticity=False for energy in energies: SM=kwant.smatrix(syst,energy=energy,check_hermiticity=False,in_leads=[0],out_leads=[0],params=dict(energy=energy,V=-1.8)) R=SM.transmission(0,0) Reflection2.append(R) pyplot.plot(energies,Reflection1,'ro',energies,Reflection2,'b-') pyplot.xlabel("energy",fontsize=20) pyplot.ylabel("R",fontsize=20) pyplot.show() On Tue, Mar 19, 2019 at 11:00 AM 张金龙 <jlzhang1996@163.com> wrote:
Dear Sir. I have a question about Kwnat. Can we calculate the systems considered with the dephasing effects by Kwant? For example, just add a non-hermite terms in the onsite potential or add the non-hermite hopping between (i,j) and (j,i) leading the Hamiltonian <http://www.baidu.com/link?url=Rnd4yLigmbBMCfnVjG44TYUu8gt0N_KWTnkcnTy1m__uGS...> no longer hermite ?
-- Jinlong Zhang jlzhang@163.com
-- Abbout Adel