[Pw_forum] electron phonon interaction in ph.x

[Jin Zhang]

I did a test in phonon.f90. The code is sth like this:

  USE ions_base, only : nat,amass
  complex(dp), allocatable :: work(:,:)
  allocate(work(3*nat,3*nat))

  DO ipert = 1,3*nat
     DO jpert = 1,3*nat
        DO i=1,3*nat
        work(ipert,jpert) = work(ipert,jpert) +
conjg(dyn(i,ipert))*amass(1)*dyn(i,jpert)
        ENDDO
     ENDDO
  ENDDO
  write(*,*) 'dynmat:'
  write(*,"(6(f12.8))") work(:,:)
  deallocate(work)
------------------------------------------
The output for example07 is:
  1.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000
  0.00000000  0.00000000  1.00000000  0.00000000  0.00000000  0.00000000
  0.00000000  0.00000000  0.00000000  0.00000000  1.00000000  0.00000000
 The relation dyn^{\diag} * amass * dyn = I sustains indeed.
 Actually we're talking about the same thing. The inner product of
eigenvector U^{\diag} M U gives scalar 1.
 While dyn^{\diag} * amass * dyn gives unit matrix.

On 12/1/06, degironc <degironc at sissa.it> wrote:
>
> Jin Zhang wrote:
>
> > 2. dyn(iat, jat): The dynamical matrix which obeys -- dyn^{\diag} *
> > amass * dyn = 1
>
> I don't think dymanical matric should obey this relation...
>
> EIGENVECTORS,  U,  of the generalized problem Dyn U = M U omega^2  will
> obey
> U^\dagger M U = 1 or something like that...
> while
> EIGENVECTORS, V=\sqrtM U of problem 1/sqrtM Dyn 1/sqrtM V = omega^2 V
> will obey V^\dagger V = 1
>
> stefano
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