[Pw_forum] question on random_matrix

[Virginie Trinité]

Thanks for your explanations

Virginie Trinite

Stefano de Gironcoli wrote:

>
> 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
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