### Abstract

We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy-level statistics of a classically chaotic system in a weak magnetic field. The generating function of spectral correlations is calculated by using the semiclassical periodic-orbit theory. An explicit calculation up to the second order, including the non-oscillatory and oscillatory terms, agrees with the prediction of random matrix theory. Formal expressions of the higher order terms are also presented. The nonlinear sigma (NLS) model of random matrix theory, in the variant of the Bosonic replica trick, is also analyzed for the crossover between the Gaussian orthogonal ensemble and Gaussian unitary ensemble. The diagrammatic expansion of the NLS model is interpreted in terms of the periodic-orbit theory.

Original language | English |
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Article number | 495101 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 49 |

DOIs | |

Publication status | Published - 2009 Dec 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(49), [495101]. https://doi.org/10.1088/1751-8113/42/49/495101