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

Abstract

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.

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