Sparse random matrix configurations for two or three interacting electrons in a random potential

Details Sparse random matrix configurations for two or three interacting electrons in a random potential Sparse random matrix configurations for two or three interacting electrons in a random potential

1997-03-20

arxiv.org/abs/cond-mat/9703188v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, Latex file, 5 postscript files

Scientific paper

10.1103/PhysRevB.56.13623

We investigate the random matrix configurations for two or three interacting electrons in one-dimensional disordered systems. In a suitable non-interacting localized electron basis we obtain a sparse random matrix with very long tails which is different from a superimposed random band matrix usually thought to be valid. The number of non-zero off-diagonal matrix elements is shown to decay very weakly from the matrix diagonal and the non-zero matrix elements are distributed according to a Lorentzian around zero with also very weakly decaying parameters. The corresponding random matrix for three interacting electrons is similar but even more sparse.

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