[Pw_forum] question on random_matrix

[Stefano de Gironcoli]

On Wed, 31 May 2006, Paolo Giannozzi wrote:
>
>  !   Create a random hermitian matrix with non zero elements
>  !   similar to the dynamical matrix of the system
>
> but this is somewhat misleading. From what I remember the
> random matrix is used to find the irreducible representations
> of the small group of q (the phonon wavevector). If no symmetry
> sends atom na into atom nb, displacements of atoms na and nb
> will belong to different irreps.
>
> Disclaimer: I didn't write, and never really understood, how
> symmetry works in the phonon code, so the above might be
> all wrong!
>
I conmfirm what Paolo says: If two atoms are not connected by a 
symmetry operation then the corresponding "random matrix element"
is actually set to zero so that they will eventually belong to different 
irreducible representations.

Irreps are needed as a basis to expand the vibrational displacement 
patterns.
The irreps chosen by the code are just one possible choice among infinite 
physically equivalent ones; technically it is convenient for efficiency 
in the calculation of the perturbation to have basis functions where as 
few as possible atoms are moved, hence the above prescription.

stefano