### Abstract

We consider a failure of the semiclassical trace formula attributable to resonant periodic orbits and quasi-integrability of the system by using the quantum standard map. We derive Gutzwiller-type semiclassical expressions of TrU and TrU^{2} lor the Floquet operator U, and compare them with quantum rigorous expressions. We demonstrate that the divergence of the formula due to resonant orbits is avoided by making use of the normal forms for the action. For a quasi-integrable case, we confirm that the semiclassical expression is also well modified.

Original language | English |
---|---|

Pages (from-to) | 1131-1138 |

Number of pages | 8 |

Journal | Journal of the Physical Society of Japan |

Volume | 68 |

Issue number | 4 |

Publication status | Published - 1999 Apr |

Externally published | Yes |

### Fingerprint

### Keywords

- Normal form
- Quantum chaos
- Standard map
- Trace formula

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*68*(4), 1131-1138.

**On the Failure and the Modification of Semiclassical Trace Formula in the Quantum Standard Map.** / Saitou, Keiji; Nagao, Taro.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 68, no. 4, pp. 1131-1138.

}

TY - JOUR

T1 - On the Failure and the Modification of Semiclassical Trace Formula in the Quantum Standard Map

AU - Saitou, Keiji

AU - Nagao, Taro

PY - 1999/4

Y1 - 1999/4

N2 - We consider a failure of the semiclassical trace formula attributable to resonant periodic orbits and quasi-integrability of the system by using the quantum standard map. We derive Gutzwiller-type semiclassical expressions of TrU and TrU2 lor the Floquet operator U, and compare them with quantum rigorous expressions. We demonstrate that the divergence of the formula due to resonant orbits is avoided by making use of the normal forms for the action. For a quasi-integrable case, we confirm that the semiclassical expression is also well modified.

AB - We consider a failure of the semiclassical trace formula attributable to resonant periodic orbits and quasi-integrability of the system by using the quantum standard map. We derive Gutzwiller-type semiclassical expressions of TrU and TrU2 lor the Floquet operator U, and compare them with quantum rigorous expressions. We demonstrate that the divergence of the formula due to resonant orbits is avoided by making use of the normal forms for the action. For a quasi-integrable case, we confirm that the semiclassical expression is also well modified.

KW - Normal form

KW - Quantum chaos

KW - Standard map

KW - Trace formula

UR - http://www.scopus.com/inward/record.url?scp=0033431382&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033431382&partnerID=8YFLogxK

M3 - Article

VL - 68

SP - 1131

EP - 1138

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 4

ER -