Spectral statistics of chaotic many-body systems

Dubertrand, Remy and Müller, Sebastian (2016) Spectral statistics of chaotic many-body systems. New Journal of Physics, 18 (3). 033009. ISSN 1367-2630

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Official URL: https://doi.org/10.1088/1367-2630/18/3/033009

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 Schrödinger (or Gross–Pitaevski) 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 Schrödinger 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.

Item Type: Article
Uncontrolled Keywords: many-body systems, semiclassical methods, quantum chaos
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Elena Carlaw
Date Deposited: 20 Nov 2019 11:47
Last Modified: 20 Nov 2019 12:00
URI: http://nrl.northumbria.ac.uk/id/eprint/41545

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