Quantum Ergodicity on Graphs
- School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
- Department of Mathematics, University of Bristol, Bristol BS8 1TW (United Kingdom)
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.
- OSTI ID:
- 21180082
- Journal Information:
- Physical Review Letters, Vol. 101, Issue 26; Other Information: DOI: 10.1103/PhysRevLett.101.264102; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0031-9007
- Country of Publication:
- United States
- Language:
- English
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