[Pw_forum] phonon eigenvectors

[Stefano Baroni]

Eric: do not be satisfied by meaningful answer to your meaningful and  
legitimate questions. You have to *understand* them (i.e. do not stop  
thinking and striving to understand, until answers given by others   
sound to you as YOUR answers. Keep asking yourself questions until  
you are sure that you can answer all of them).

Signed: Grandad

Coming now to your present doubt. You have to understand here that  
what is arbitrary here is the overall _phase_ of the eigenvectors.  
This obviously implies (in some sense) that the imaginary part is  
arbitrary, but *NOT* that it can (always) be neglected, as this  
specic case  shows. What has to be nonzero is NOT the real part of  
the eigenvector, but its modulus.

Is it clearer now? Could you answer similar questions by yourself in  
the future?

Signed: Stefano B.


On Aug 31, 2006, at 6:07 AM, Eric Abel wrote:

> Hello PWSCF users,
>
> I have a question which is sort of a follow-up to a similar  
> question which I asked previously.  Anyway, I was wondering about  
> the imaginary part of the phonon eigenvectors, which at the time,  
> Stefano had informed me are more or less arbitrary.   At the time  
> that made sense.  But now I am trying to make sense of the  
> following eigenvectors:
>
> q =       0.0000      0.0563      0.0000
> ********************************************************************** 
> ****
>     omega( 1) =      -0.308036 [THz] =     -10.275037 [cm-1]
> (  0.000000   0.000000     0.000000  -0.142674    -0.338669    
> 0.000000   )
> (  0.000000   0.000000     0.031918  -0.201463    -0.388896   
> -0.061613   )
> (  0.000000   0.000000     0.019612  -0.123787    -0.367551   
> -0.058231   )
> (  0.000000   0.000000     0.000000  -0.226888    -0.354765    
> 0.000000   )
> (  0.000000   0.000000     0.036445  -0.230039    -0.328252   
> -0.052005   )
> (  0.000000   0.000000     0.000000  -0.096682    -0.403396    
> 0.000000   )
>     omega( 2) =       0.617574 [THz] =      20.600196 [cm-1]
> ( -0.403925  -0.012145     0.000000   0.000000     0.000000    
> 0.000000   )
> ( -0.397050  -0.075201     0.000000   0.000000     0.000000    
> 0.000000   )
> ( -0.397199  -0.075229     0.000000   0.000000     0.000000    
> 0.000000   )
> ( -0.404073  -0.012149     0.000000   0.000000     0.000000    
> 0.000000   )
> ( -0.408949  -0.077455     0.000000   0.000000     0.000000    
> 0.000000   )
> ( -0.416112  -0.012511     0.000000   0.000000     0.000000    
> 0.000000   )
>     omega( 3) =       0.788199 [THz] =      26.291668 [cm-1]
> (  0.000000   0.000000     0.000000   0.389819    -0.233273    
> 0.000000   )
> (  0.000000   0.000000    -0.055122   0.347926    -0.110454   
> -0.017499   )
> (  0.000000   0.000000    -0.061881   0.390589    -0.148121   
> -0.023467   )
> (  0.000000   0.000000     0.000000   0.342277    -0.187111    
> 0.000000   )
> (  0.000000   0.000000    -0.050913   0.321357    -0.249835   
> -0.039581   )
> (  0.000000   0.000000     0.000000   0.384275    -0.092029    
> 0.000000   )
>
> These are the first 3 (accoustic) modes of the spectrum.  If the  
> imaginary part doesn't matter, then it would appear that the  
> accoustic displacement along the b-direction is practically zero.   
> However, the imaginary part is the same magnitude as the  
> displacements in the other orthogonal directions.  Is there any  
> physical meaning to this, or is it just an artifact of the  
> calculation?
>
> Eric,
> Ph.D. Student, M.I.T.
>
>
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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