Berkolaiko, G. (2004) Form factor for large quantum graphs: evaluating orbits with time-reversal. Waves in Random Media, 14. S7-S27. ISSN 0959-7174Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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|
|Depositing user:||Strathprints Administrator|
|Date Deposited:||17 Nov 2006|
|Last modified:||29 Apr 2016 07:36|