Re: [Kwant] Kwant-discuss Digest, Vol 20, Issue 4
Dear Xavier,
Thanks a lot for the reply. It is very clear for me now.
Regards,
Kwok-Long Lee
On Mon, Apr 13, 2015 at 8:01 PM,
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Today's Topics:
1. Re: about ldos and wave function probability (Xavier Waintal)
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Message: 1 Date: Mon, 13 Apr 2015 10:06:21 +0200 From: Xavier Waintal
To: Lee Kwok-Long Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] about ldos and wave function probability Message-ID: <15D07A0E-01BF-493E-A3AA-071571C396FD@cea.fr> Content-Type: text/plain; charset=iso-8859-1 Dear Kwo-Long,
Le 11 avr. 2015 à 07:41, Lee Kwok-Long
a écrit : Dear all, I am learning Kwant through the tutorials and published paper, but I feel confused about some Kwant scripts below: 1)Tutorial 2.7.1. ham = sys.hamiltonian_submatrix() evecs = la.eigh(ham)[1] wf = abs(evecs[:, n])**2 2)New Jour nal of Physics 16(2014) 063065 figure14: wf=kwant.wave_function(sys, energy, args) return(abs(wf(lead_nr))**2).sum(axis=0) 3)New Jour nal of Physics 16(2014) 063065 figure4: local_dos = kwant.ldos(sys, energy=. 2) kwant.plotter.map(sys, local_dos, num_lead_cells=10) My questions are: Does "evecs = la.eigh(ham)[1]" give the same wave function as "wf=kwant.wave_function(sys, energy, args)"?
The first one simply calculates the eigenvectors of a FINITE system using standard diagonalization routines (as found in numpy - not in Kwant). The second calculates the scattering eigenfunctions of an INFINITE system with leads at energy= energy (The latter belong to a continuum).
What is the definition of local_dos?
The usual one, i.e. ldos(E,r)= sum_a |wf_a(a)|^2 delta(E-E_a) where wf_a and E_a are the eigen functions/energy of the system
Does"local_dos = kwant.ldos(sys, energy=. 2)" give the same results as "wf = abs(evecs[:, n])**2"?
Yes up to a factor 1/2pi. kwant.ldos is a simpler wrapper around kwant.wave_function(). Please have a look at the source code.
Best, Xavier
Could you help me to know the differences and similarities? Kwok-Long Lee
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