Particle diagrams and embedded many-body random matrix theory

Rupert A Small, Sebastian Muller

Research output: Contribution to journalLetter (Academic Journal)peer-review

4 Citations (Scopus)


We present a 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 of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k≤m) 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 semicircular 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.
Original languageEnglish
Article number010102(R)
Number of pages4
JournalPhysical Review E: Statistical, Nonlinear, and Soft Matter Physics
Issue number010102(R)
Publication statusPublished - 25 Jul 2014


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