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

Fan, Yiyun; Gnutzmann, Sven; Liang, Yuqi

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.

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), https://doi.org/10.1103/PhysRevE.96.062207

• Journal Article Type: Article
• Acceptance Date: Nov 28, 2017
• Online Publication Date: Dec 13, 2017
• Deposit Date: Dec 15, 2017
• Publicly Available Date: Dec 15, 2017
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 96
• Issue: 6
• DOI: https://doi.org/10.1103/PhysRevE.96.062207
• Keywords: Quantum chaos
• Public URL: https://nottingham-repository.worktribe.com/output/899945
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.96.062207
• Contract Date: Dec 15, 2017