[Wien] why we need to divide plasma frequency by root(2)?

[Gavin Abo]

Thanks.

So if understand correctly, the w_pl^2(up-spin) is what is outputted in 
case.outputjointup for a spin-polarized spin orbit calculation by line 
859 of joint.f in the post:

https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg16552.html

So, w_pl^2(dn-spin) = w_pl^2(up-spin).  Plugging that into the SP 
(without spin orbit) plasma frequency equation from your post below:

w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(up-spin) )
w_pl = sqrt(2*w_pl^2(up-spin) )
w_pl = sqrt(2)*w_pl(up-spin)  <= This showing why we need to get rid of 
the sqrt(2) by dividing the sqrt(2)*w_pl(up-spin) by the sqrt(2) to get 
the plasma frequency w_pl equal to w_pl(up-spin).

So one needs to calculate (w_pl^2(up-spin) + w_pl^2(up-spin))/sqrt(2) 
[or (2*w_pl^2(up-spin))/sqrt(2)] to get the plasma frequency like in the 
post at:

https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg16017.html

So the mistake I made was the missing multiplication by 2 in my previous 
post:

https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg16615.html

2*2.074/sqrt(2) 2*2.074/sqrt(2) 2*1.264/sqrt(2)

or

2.933 2.933 1.788

Or do I still have something not quite right?

On 10/27/2017 12:44 AM, Fecher, Gerhard wrote:
> The optics programm tells about the SP Plasma frequencies:
> w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(dn-spin) )
>
> where does this come from
> remember the classical approach where the plasma frequency is proportional to root(n) with n being the density of free electrons (number of electrons per Volume)
> now what do you have in the SP case ? Shouldn't that be root/n_up+n_dn) ?
> The programm however delivers  w_up proportional to root(n_up) and w_dn prop to root(n_dn) and you see where the above equation is comming from
>
> Finally show what happens when the two densities are equal  n_up=n_dn and you see where the root(2) is coming from and when to use it
>
> (Note that the root(2) is here not because of surface plasmons)
>
> Ciao
> Gerhard
>
> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
> "I think the problem, to be quite honest with you,
> is that you have never actually known what the question is."
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Inorganic and Analytical Chemistry
> Johannes Gutenberg - University
> 55099 Mainz
> and
> Max Planck Institute for Chemical Physics of Solids
> 01187 Dresden
> ________________________________________
> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Gavin Abo [gsabo at crimson.ua.edu]
> Gesendet: Sonntag, 22. Oktober 2017 00:42
> An: wien at zeus.theochem.tuwien.ac.at
> Betreff: Re: [Wien] why we need to divide plasma frequency by root(2)?
>
> I could be wrong, but I think you just need to take the sqrt(2) of each plasma frequency:
>
> 2.074/sqrt(2) 2.074/sqrt(2) 1.264/sqrt(2)
>
> then put them in case.inkram (not case.injoint).
>
> You should be able to use multiple plasma frequencies in case.inkram but don't forget to add a Gamma for drude value for each of the plasma frequencies [ https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14495.html ].
>
> On 10/21/2017 4:29 PM, Dr. K. C. Bhamu wrote:
>
> ---------------------case.injoint
> xx
> xx
> 1                                              >> correction
> 2.0740      2.0740      1.2640
> xx
> -----------------------------------
>
> were xx means no change in lines of case.inkram.
>
>
>
> At page numer  164 under section "8.11 KRAM (Kramers-Kronig transformation) in UG"
>
>
> "For a metal, the Plasma-frequencies (intraband transitions) for up and dn should be added, but then divided by√2, before using x kram."
>
> Does it mean that we need to add all three components and then divide by root(2) and put a single number [(2.074+2.074+1.264)/root(2)=3.88] instead of all three in case.injoint?
>
>
> kind regards
>
> Bhamu
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> SEARCH the MAILING-LIST at:  http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://zeus.theochem.tuwien.ac.at/pipermail/wien/attachments/20171027/30e78ff9/attachment.html>