[Pw_forum] Transmission calculation using PWCOND

[Manoj Srivastava]

Thank you Alexander!

-Manoj
On Fri, 3 Apr 2009, Alexander Smogunov wrote:

> Dear Manoj
> 
> On Wednesday 01 April 2009 22:57, Manoj Srivastava wrote:
> > Dear PWSCF users and developers,
> >  I have been trying to understand the PWCOND code for transmission
> > calculation, basically 'transmit.f90' file. The wavefunction in the left
> > lead, right lead and scattering region is given by -
> >
> >        psi_k+sum_{k'}r_{kk'}psi_k'
> >   psi= sum_{n} a_n psi_n+ sum_{\alpha l m} C_{\alpha l m}psi_{\alpha l m}
> >        sum_{k'}t_{kk'}psi_k'
> >
> > The above expression is from Choi & Ihm's paper, on which I believe PWCOND
> > is based on. Now undetermined coefficients in above expression are
> > r_{kk'}, a_n, C_{\alpha,l,m}, t_kk'. I am confused on code evaluates these
> > coefficients.  My understanding is you first get the wavefunction in the
> > leads and then solve scattering region the same way to get the
> > wavefunction in scattering region, so at this point you have already
> > determined a_n and C_{\alpha,l,m}. At last do boundary matching condition
> > between leads and scattering region to get reflection and transmission
> > coefficient. Am I right? 
> No, the scattering state (SS)  is completely determined by unknown 
> coefficients which are: {r_kk', a_n, a_alpha, t_kk'}, the first defines the 
> SS in the left lead, the two next in the scattering region, and the last one 
> in the right lead. What you have found before are just basis solutions phi_n 
> and phi_alpha of the Sroedinger eq. in the scattering region over which you 
> expand the SS with coefficients (unknown yet) a_n and a_alpha.
> 
> Hope this helps,
> Alexander
> 
> > My thinking is based on simple quantum mechanics 
> > scattering problem where we solve schrodinger's equation in each region
> > and then do boundary matching to get reflection and transmission
> > coefficients.
> >
> > Now looking at the subroutine 'transmit.f90', this does not appear to be
> > the case. It seems as if we are solving the Schrodinger's equation in the
> > scattering region and doing boundary matching at the same time. Using a
> > big matrix and solving something like AX=B. Would anybody mind explaing
> > what's going on in subroutine transmit.f90?
> >
> > Regards,
> > Manoj Srivastava
> > Physics Graduate Student
> > University Of Florida, Gainesville, FL
> >
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