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

Fan, Yiyun and Gnutzmann, Sven and Liang, Yuqi (2017) Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops. Physical Review E, 96 (6). 062207. ISSN 1539-3755

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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.

Item Type: Article
Keywords: Quantum chaos
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1103/PhysRevE.96.062207
Depositing User: Gnutzmann, Sven
Date Deposited: 15 Dec 2017 09:51
Last Modified: 15 Dec 2017 09:55
URI: http://eprints.nottingham.ac.uk/id/eprint/48762

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