[Pw_forum] Transmission calculation using PWCOND
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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[Pw_forum] Transmission calculation using PWCOND
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
>
> ___
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://www.democritos.it/mailman/listinfo/pw_forum
[Pw_forum] Transmission calculation using PWCOND
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? 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
