Quantum Ergodicity on Graphs
Quantum Ergodicity on Graphs
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DOI：
10.1103/physrevlett.101.264102
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发表时间：
2008-12-31
影响因子：
8.6
通讯作者：
Piotet, F.
中科院分区：
文献类型：
--
作者：
Gnutzmann, S.;Keating, J. P.;Piotet, F.
研究了高能极限下量子图上本征函数的等分布。我们的主要结果是对大型良好连通图的均分布偏差的估计。我们用一个精确的场理论表达式来表示超对称非线性模型的一个变体。我们的估计是基于这个表达式的鞍点分析，并导致一个准则，当均匀分布出现在大图的极限渐近。我们的理论预测了收敛速度，这是对先前估计的重要改进，长期以来被认为对量子混沌系统有效，在某些情况下与它们一致，但不是全部。我们讨论了用数值方法验证理论的具体例子。
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.