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Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops

Fan, Yiyun; Gnutzmann, Sven; Liang, Yuqi

Authors

Yiyun Fan

Sven Gnutzmann sven.gnutzmann@nottingham.ac.uk

Yuqi Liang



Abstract

We consider two coupled quantum tops with angular momentum vectors L and M. The coupling Hamiltonian defines the Feingold-Peres model, which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems, which extends the well-known threefold way of Wigner and Dyson (referred to as “standard” symmetry classes here). We identify the nonstandard symmetry classes BDI0 (chiral orthogonal class with no zero modes), BDI1 (chiral orthogonal class with one zero mode), and CI (antichiral orthogonal class) as well as the standard symmetry class AI (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue, we show that the Feingold-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mix and near-integrable classical dynamics, we show that these signatures disappear or strongly change.

Journal Article Type Article
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 1539-3755
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 6
APA6 Citation Fan, Y., Gnutzmann, S., & Liang, Y. (in press). Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops. Physical Review E, 96(6), doi:10.1103/PhysRevE.96.062207
DOI https://doi.org/10.1103/PhysRevE.96.062207
Keywords Quantum chaos
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.062207
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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