[Octopus-devel] [Octopus-notify] svn commit: r3102 - in trunk/src: utils by acastro

[alberto.castro at tddft.org]

Hi,

I am not sure, maybe you are right. What I had in mind when I did this
change was the following scheme:



The "kick" that we perform amounts to using a Hamiltonian in the form:

	H(t) = H_0 + V(t) = H_0 - \lambda Q \delta(t)

and, up to now, we have always assumed that Q is a dipole operator;
therefore the V(t) has the following form -- keeping all the constants
so tat the dimensions are more clear:

V(\vec{r}, t) = - \lambda (\hbar/a_0) \hat{p} * \vec{r} \delta(t)

where \hat{p} is a unit dimensionless vector. Note that the delta
function carries dimensions of 1/[T]. In this way, \lambda is just a
dimensionless constant that changes the strength of the perturbation. But
one could have more general kick functions (this is the addition I have
recently put):

V (\vec{r}, t) = - \lambda * V_{lm}(\vec{r}) * \delta(t) =
    - \labmda * (\hbar/a_0^l) r^l Y_{lm}(\vec{r}) * \delta(t)

and, in the most general case, a combination (not coded yet):

V (\vec{r}, t) = - \lambda * \sum_{lm} w_{lm} V_{lm}(\vec{r}) \delta(t)

where the w_{lm} are dimensionless "weights".

What we had before, when \lamda was not dimensionless, was something like
(for the dipole case):

V(\vec{r}, t) = - \labmda \hbar \hat{p} * \vec{r} \delta(t)

so that \lambda had dimensions of 1/[L]. But then we would need that
lambda, for V_{lm}, would carry dimensions of 1/[L]^l. And for the case
of a linear combination, one would have to put the dimensions into the
weights, and leave \lambda dimensionless.... (or not have any \lambda at
all). At the end I thought that it would be easier to code, and to
understand -- if properly documented -- to have lambdas and w's
dimensionless...

Al.

>   Hi,
>
>   Two very small comments:
>
>   *) adimensional -> dimensionless
>
>   *) By removing the conversion line, what we have now is not
> dimensionless at all, I think! It is simply in atomic units. Are you
> sure that this is desirable? Actually, I believe that it makes things
> more complicated and inconsistent...
>
>   cheers,
>   Miguel
>
> On Wed, 2007-07-25 at 13:17 +0100, octopus-notify at tddft.org wrote:
> >       Author: acastro
> >         Date: Wed Jul 25 13:16:59 2007
> > New Revision: 3102
> >    Changeset: http://www.tddft.org/trac/octopus/changeset/3102
> >
> > Modified:
> >    trunk/src/td/spectrum.F90
> >    trunk/src/utils/oscillator_strength.F90
> >
> > Log:
> > Fixed a couple of bugs in the oct-oscillator-strength utility.
> >
> > Also, now the "delta_strength" will be considered to be adimensional
> > (otherwise, one would have to take care of differente units if one
> > uses a dipole, quadrupole kick, etc.  I think it will be easier this
> > way.
> >
> >
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> >
>
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>

======================================================================
Dr. Alberto Castro

Institut fur Theoretisch Physik, Freie Universitat Berlin.
Arnimallee, 14, Berlin 14195 (Deutschland)

Tel:   +49 30 83853028
Fax:   +49 30 83855258
skype: alberto_c_barrigon
email: alberto at physik.fu-berlin.de
======================================================================