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• W2012068372 abstract "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." @default.
• W2012068372 created "2016-06-24" @default.
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• W2012068372 date "2008-12-29" @default.
• W2012068372 modified "2023-10-01" @default.
• W2012068372 title "Quantum Ergodicity on Graphs" @default.
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• W2012068372 doi "https://doi.org/10.1103/physrevlett.101.264102" @default.
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