20th GAMM-Seminar Leipzig on
Numerical Methods for Non-Local Operators

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
  Abstracts ->
  All seminars  
  All proceedings  
  Abstract Heinz-Jürgen Flad, Thu, 16.30-17.00 Previous Contents Next  
  Oscillating Kernels in Electronic Structure Calculations
Heinz-Jürgen Flad (MPI Leipzig)

Due to Pauli's principle, electronic structure calculations have to deal with various types of oscillations. Strong oscillations are restricted to comparatively small regions around nuclei and can be efficiently treated, at least approximately, by a variety of techniques which are briefly reviewed. More severe are weak oscillations which extend over the whole system. In our approach to electronic structure calculations, we separate the many-electron problem into asymptotically smooth kernel functions, like the Coulomb interaction and Jastrow factors, and an oscillating kernel function corresponding to the one-particle density matrix. For insulators and semiconductor like materials, the oscillations are damped by the exponential decay of the density matrix. This is not the case for metals where only an algebraic decay of the density matrices can be observed. We discuss the interactions between these kernel functions in terms of Feynman like diagrams. The possibility of sparse wavelet representations for certain types of diagrams is considered for a simplified model problem and the homogeneous electron gas.

    Previous Contents Next  

Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
Valid HTML 4.0!