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

Gregory Berkolaiko·Holger Schanz·Robert S. Whitney
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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 $-2τ^2$ to the form factor which agrees with random-matrix theory.

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Gregory Berkolaiko, Holger Schanz, Robert S. Whitney. 2002-02-13. The Leading Off-Diagonal Correction to the Form Factor of Large Graphs. https://doi.org/10.1103/physrevlett.88.104101

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