Form factor for large quantum graphs: evaluating orbits with time-reversal

Details Form factor for large quantum graphs: evaluating orbits with time-reversal Form factor for large quantum graphs: evaluating orbits with time-reversal

2003-05-07

arxiv.org/abs/nlin/0305009v2

Waves in Random Media 14 S7-S27 (2004)

Nonlinear Sciences

Chaotic Dynamics

25 pages, 14 figures, accepted to Waves in Random Media (special issue on Quantum Graphs and their Applications). Fixed typos,

Scientific paper

10.1088/0959-7174/14/1/008

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 \tau 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 contribution 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, it is more algorithmical and more system-independent, making possible future applications of the technique to systems other than quantum graphs.

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