Leading off-diagonal correction to the form factor of large graphs.
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 -2tau(2) to the form factor which agrees with random-matrix theory.
Berkolaiko
Gregory
G
The Weizmann Institute of Science, Rehovot 76100, Israel.
Schanz
Holger
H
Whitney
Robert S
RS