Abstract
We present a method which uses Feynmanlike diagrams to calculate the statistical quantities of embedded manybody 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 mbody system with k fermions or bosons interacting through a random Hermitian potential (k≤m) in the limit where the number of possible singleparticle 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 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
Original language  English 

Article number  010102(R) 
Number of pages  4 
Journal  Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 
Volume  90 
Issue number  010102(R) 
Publication status  Published  25 Jul 2014 
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Dr Sebastian Muller
 School of Mathematics  Senior Lecturer
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member