### 抜粋

The spectral correlation of a chaotic system with spin 1/2 is universally described by the GSE (Gaussian symplectic ensemble) of random matrices in the semiclassical limit. In semiclassical theory, the spectral form factor is expressed in terms of the periodic orbits and the spin state is simulated by the uniform distribution on a sphere. In this paper, instead of the uniform distribution, we introduce Brownian motion on a sphere to yield the parametric motion of the energy levels. As a result, the small time expansion of the form factor is obtained and found to be in agreement with the prediction of parametric random matrices in the transition within the GSE universality class. Moreover, by starting the Brownian motion from a point distribution on the sphere, we gradually increase the effect of the spin and calculate the form factor describing the transition from the Gaussian orthogonal ensemble class to the GSE class.

元の言語 | English |
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記事番号 | 004 |

ページ（範囲） | 12055-12070 |

ページ数 | 16 |

ジャーナル | Journal of Physics A: Mathematical and Theoretical |

巻 | 40 |

発行部数 | 40 |

DOI | |

出版物ステータス | Published - 2007 10 5 |

外部発表 | Yes |

### フィンガープリント

### ASJC Scopus subject areas

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

### これを引用

*Journal of Physics A: Mathematical and Theoretical*,

*40*(40), 12055-12070. [004]. https://doi.org/10.1088/1751-8113/40/40/004