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[Matthieu Verstraete <mjv500@york.ac.uk>]

> Yes. I understand that the thermalization of hot electrons is
> typically fast, on the scale of tens femtoseconds whereas the
> relaxation of hot electron energy to the lattice in metals is much
> slower, on ps scale. The question that I intended to ask was: if we
> assume the establishment of a homogenous hot electron temperature
> (electrons have thermalized themselves and formed a fermi
> distribution) and look at the equilibration process of electron with
> lattice, can we take the matrix element from previous GS calculation
> as the electron-phonon interaction at this stage? I presume one need
> to calculation at non-zero fermi temperature to obtain these elements
> as setting a combination of tsmear and occopt=3 in the smearing for
> metals like what you mentioned below?
Ok - excellent question. Yes: the states will be different due to the 
differing high T density you get, and the perturbed potential will be too. 
This is definitely the best approximation you can get from the standard 
code. There could be additional terms coming from the perturbation of the 
entropic term, but this is probably less of a worry (small and probably 
fine). Setting the smearing in elphon to the same value is a bit off, as 
it uses a gaussian smearing (only supposed to be doing kpoint integration, 
not real temperature). You could modify the routine (probably elphon.F90) 
to use a Fermi Dirac smearing function, or adjust the smearing width to 
get a rough equivalent to the thermal function.

obviously once the phonons kick in and/or the lattice expands the matrix 
elements you calculate will be further and further from the correct ones, 
but will probably still be quite good.

> Yes. That is exactly what I meant. But roughly the matrix element
> varies as 1/(q+G)^2. So that value might be quite small though.
I think this is correct, but I'm still not sure we are even neglecting 
them. Have to sit down and do the equations...

very interesting stuff;

Matthieu