Particle diagrams and embedded many-body random matrix theory

Understand

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.