Quantum ergodicity on graphs

S Gnutzman, JP Keating, F Piotet

Research output: Contribution to journalArticle (Academic Journal)peer-review

14 Citations (Scopus)


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 σ 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.
Translated title of the contributionQuantum ergodicity on graphs
Original languageEnglish
Pages (from-to)264102 - 264105
Number of pages7
JournalPhysical Review Letters
Volume101, issue 26
Publication statusPublished - Dec 2008

Bibliographical note

Publisher: Oxford University Press

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