The Leading Off-Diagonal Correction to the Form Factor of Large Graphs

Details The Leading Off-Diagonal Correction to the Form Factor of Large Graphs The Leading Off-Diagonal Correction to the Form Factor of Large Graphs

2001-07-24

arxiv.org/abs/nlin/0107056v2

Phys. Rev. Lett. 88 (2002) 104101

Nonlinear Sciences

Chaotic Dynamics

5 pages (2 figs). Version to appear in PRL [RevTeX4] - with a bonus appendix for nlin.CD users

Scientific paper

10.1103/PhysRevLett.88.104101

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, $K(\tau)$, 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 $-2\tau^2$ to the form factor which agrees with random-matrix theory.

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