Spectral statistics of chaotic many-body systems

Remy Dubertrand, Sebastian Muller

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

21 Citations (Scopus)
308 Downloads (Pure)

Abstract

We derive a trace formula that expresses the level density of chaotic many-body 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 Bose-Hubbard 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 many-particle systems becomes universal and agrees with predictions from the Wigner-Dyson ensembles of random matrix theory. The conditions for Wigner-Dyson statistics involve a gap in the spectrum of the Frobenius-Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.
Original languageEnglish
Article number033009
Number of pages19
JournalNew Journal of Physics
Volume18
Early online date2 Mar 2016
DOIs
Publication statusPublished - Mar 2016

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