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.
Original language | English |
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Pages (from-to) | S7-S27 |
Journal | Waves in Random Media |
Volume | 14 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2004 |
Keywords
- quantum graphs
- time-reversal
- periodic-orbit theory
- mathematics