Berkolaiko, G. (2004) *Form factor for large quantum graphs: evaluating orbits with time-reversal.* Waves in Random Media, 14. S7-S27. ISSN 0959-7174

## Abstract

It has been shown that for a certain special type of quantum graphs the random-matrix form factor can be recovered to at least third order in the scaled time t using periodic-orbit theory. Two types of contributing pairs of orbits were identified: those which require time-reversal symmetry and those which do not. We present a new technique of dealing with contributions from the former type of orbits. The technique allows us to derive the third-order term of the expansion for general graphs. Although the derivation is rather technical, the advantages of the technique are obvious: it makes the derivation tractable, it identifies explicitly the orbit configurations which give the correct contribution and it is more algorithmic and more system-independent, making possible future applications of the technique to systems other than quantum graphs.

Item type: | Article |
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ID code: | 2117 |

Keywords: | quantum graphs, time-reversal, periodic-orbit theory, mathematics, Mathematics, Physics and Astronomy(all) |

Subjects: | Science > Mathematics |

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

Related URLs: | |

Depositing user: | Strathprints Administrator |

Date Deposited: | 17 Nov 2006 |

Last modified: | 04 Sep 2014 12:09 |

URI: | http://strathprints.strath.ac.uk/id/eprint/2117 |

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