/plasmon-cpp

Tools to calculate quantities related to plasmons in materials with no translational symmetry.

Primary LanguageC++MIT LicenseMIT

This repository contains the code for my Bachelor thesis. There is some (incomplete) documentation of C++ code in the docs directory and README.pdf contains some explanation of the underlying physical theory.

The following list contains some questions I could find no answer to yet. I'd really appreciate it if you could have a look at them and maybe help me out.

Questions

  1. In RPA, we use perturbation potential of the form V*exp(-i * omega * t + eta * t). Why is V taken to be diagonal in position representation? This assumtion seems logical for some cases. Consider, for example, constant external electric field E. Then V(r) = -q * E . r, which is, by definition, diagonal. The same holds for applied magnetic field B(r). But does this hold in general?

Answer: I spoke to Mikhail Katsnelson today, he confirmed that V is usually diagonal.

  1. Have a look at the derivation in footnote 3. What is the Fourier transform of it? Factor exp(eta * t) results in divergencies in Fourier integral... Or is there a mistake in my calculations? Maple, for example is able to calculate the transform of exp(-i * omega * t) * (1 + eta * t). Here, I used the Taylor expansion of exp. The result is 2 * Pi * (I * eta * Dirac(1, omega) + Dirac(omega)). This is a really nice, because then we can neglect the first delta function under the assumption that eta is small. Unfortunately, I failed to derive this expression myself and I don't really trust my knowledge of Maple in this case.

Answer: There is a rather nice description of this concept in "Causality and Dispertion Relations" book by H.M. Nussenzveig. The method's description should now be correct -- see updated PDF.

  1. We do all the calculations in the atomic basis, i.e. a basis spanned by local site wave functions.I wonder, is this basis actually complete? What would be a good explanation for it? Is this because we use tight-binding approximation? In the sense that electrons are "tight" to atoms and thus local site functions + linear combinations thereof give us all possible states? Answer: Yes.