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Abstract
We derive a trace formula that expresses the level density of chaotic manybody systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrodinger equation. Our formula applies to bosonic systems with discretised positions, such as the BoseHubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrodinger equation. We show that in the limits taken the statistics of fully chaotic manyparticle systems becomes universal and agrees with predictions from the WignerDyson ensembles of random matrix theory. The conditions for WignerDyson statistics involve a gap in the spectrum of the FrobeniusPerron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.
Original language  English 

Article number  033009 
Number of pages  19 
Journal  New Journal of Physics 
Volume  18 
Early online date  2 Mar 2016 
DOIs  
Publication status  Published  Mar 2016 
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Dr Sebastian Muller
 School of Mathematics  Senior Lecturer
 Applied Mathematics
 Mathematical Physics
Person: Academic , Member