%0 Journal Article
%T Particle diagrams and embedded many-body random matrix theory
%A Rupert Small
%A Sebastian M¨šller
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevE.90.010102
%X We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth and eighth moments of the level density for k fermions or bosons interacting through a random hermitian potential in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semi-circular level density to gaussian moments. The results also reveal a striking feature; the domain of the 2n'th moment is naturally divided into n subdomains specified by the points 2k = m, 3k = m, ..., nk = m.
%U http://arxiv.org/abs/1401.0318v2