### 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 |
---|---|

Article number | 495101 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 49 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

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

**Semiclassical theory for universality in quantum chaos with symmetry crossover.** / Saitou, Keiji; Nagao, Taro; Müller, Sebastian; Braun, Petr.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 49, 495101. https://doi.org/10.1088/1751-8113/42/49/495101

}

TY - JOUR

T1 - Semiclassical theory for universality in quantum chaos with symmetry crossover

AU - Saitou, Keiji

AU - Nagao, Taro

AU - Müller, Sebastian

AU - Braun, Petr

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=73249114071&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73249114071&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/49/495101

DO - 10.1088/1751-8113/42/49/495101

M3 - Article

AN - SCOPUS:73249114071

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 49

M1 - 495101

ER -