### Abstract

Language | English |
---|---|

Pages | 75-79 |

Number of pages | 5 |

Journal | Physica Scripta |

Volume | T90 |

DOIs | |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- chaotic classical dynamics
- periodic orbit
- random matrix theory
- quantum statistics

### Cite this

*Physica Scripta*,

*T90*, 75-79. https://doi.org/10.1238/Physica.Topical.090a00075

}

*Physica Scripta*, vol. T90, pp. 75-79. https://doi.org/10.1238/Physica.Topical.090a00075

**Non-universality of chaotic classical dynamics : implications for quantum chaos.** / Wilkinson, M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Non-universality of chaotic classical dynamics

T2 - Physica Scripta

AU - Wilkinson, M.

PY - 2001

Y1 - 2001

N2 - It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal agreement between their quantum spectral statistics and random matrix theory. It is argued that no such universality exists. Two statistical properties of long period orbits are considered. The distribution of the phase-space density of periodic orbits of fixed length is shown to have a log-normal distribution. Also, a correlation function of periodic-orbit actions is discussed, which has a semiclassical correspondence to the quantum spectral two-point correlation function. It is shown that bifurcations are a mechanism for creating correlations of periodic-orbit actions. They lead to a result which is non-universal, and which in general may not be an analytic function of the action difference.

AB - It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal agreement between their quantum spectral statistics and random matrix theory. It is argued that no such universality exists. Two statistical properties of long period orbits are considered. The distribution of the phase-space density of periodic orbits of fixed length is shown to have a log-normal distribution. Also, a correlation function of periodic-orbit actions is discussed, which has a semiclassical correspondence to the quantum spectral two-point correlation function. It is shown that bifurcations are a mechanism for creating correlations of periodic-orbit actions. They lead to a result which is non-universal, and which in general may not be an analytic function of the action difference.

KW - chaotic classical dynamics

KW - periodic orbit

KW - random matrix theory

KW - quantum statistics

U2 - 10.1238/Physica.Topical.090a00075

DO - 10.1238/Physica.Topical.090a00075

M3 - Article

VL - T90

SP - 75

EP - 79

JO - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

ER -