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Leading off-diagonal correction to the form factor of large graphs

Berkolaiko, G. and Shanz, H. and Whitney, R.S. (2002) Leading off-diagonal correction to the form factor of large graphs. Physical Review Letters, 88 (10). p. 104101.

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Abstract

Using periodic-orbit theory beyond the diagonal approximation we investigate the form factor, K(τ), 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 -2τ2 to the form factor which agrees with random-matrix theory.