Abstract
We present a method using Feynmanlike diagrams to calculate the statistical properties of random manybody potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the method of supersymmetry and the eigenvector expansion technique pioneered in Benet et al. (2001). We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with m bosons or fermions that interact through a random kbody Hermitian potential (k≤m); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble (eGUE) (Mon and French, 1975). Our results apply in the limit where the number l of available singleparticle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semicircular level density for m<2k to Gaussian moments in the dilute limit k≪m≪l. Regarding the form of this transition, we see that as m is increased, more and more diagrams become relevant, with new contributions starting from each of the points m=2k,3k,…,nk for the 2nth moment.
Original language  English 

Pages (fromto)  269–298 
Number of pages  20 
Journal  Annals of Physics 
Volume  356 
Early online date  14 Mar 2015 
DOIs  
Publication status  Published  May 2015 
Keywords
 particle diagrams
 random matrix theory
 MANYBODY
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Dr Sebastian Muller
 School of Mathematics  Senior Lecturer
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member