Quantum ergodicity on graphs

Details Quantum ergodicity on graphs Quantum ergodicity on graphs

2008-08-29

arxiv.org/abs/0808.4110v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.101.264102

We investigate the equidistribution of the eigenfunctions on quantum graphs in the high-energy limit. Our main result is an estimate of the deviations from equidistribution for large well-connected graphs. We use an exact field-theoretic expression in terms of a variant of the supersymmetric nonlinear sigma-model. Our estimate is based on a saddle-point analysis of this expression and leads to a criterion for when equidistribution emerges asymptotically in the limit of large graphs. Our theory predicts a rate of convergence that is a significant refinement of previous estimates, long-assumed to be valid for quantum chaotic systems, agreeing with them in some situations but not all. We discuss specific examples for which the theory is tested numerically.

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