# Leading off-diagonal correction to the form factor of large graphs

Berkolaiko, G. and Shanz, H. and Whitney, R.S.
(2002)
*Leading off-diagonal correction to the form factor of large graphs.*
Physical Review Letters, 88 (10).
p. 104101.

Official URL: http://dx.doi.org/10.1103/PhysRevLett.88.104101

## Abstract

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, K(τ), of a generic quantum graph with mixing classical dynamics and time-reversal symmetry. We calculate the contribution from pairs of self-intersecting orbits that differ from each other only in the orientation of a single loop. In the limit of large graphs, these pairs produce a contribution -2τ2 to the form factor which agrees with random-matrix theory.

Item type: | Article |
---|---|

ID code: | 2058 |

Keywords: | periodic-orbit theory, random-matrix theory, graphs, Mathematics, Physics and Astronomy(all) |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics > Mathematics |

Depositing user: | Strathprints Administrator |

Date Deposited: | 14 Jan 2007 |

Last modified: | 29 Apr 2016 07:28 |

URI: | http://strathprints.strath.ac.uk/id/eprint/2058 |

Altmetric