Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
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DOI：
10.1016/j.chaos.2016.06.012
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发表时间：
2016-01
影响因子：
7.8
通讯作者：
Jiaozi Wang;Wen-ge Wang
中科院分区：
文献类型：
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作者：
Jiaozi Wang;Wen-ge Wang
我们研究能量本征函数 (EF) 的非微扰部分中各分量的统计分布，这是 EF 的主体所在。我们在五个模型中的数值模拟表明，分布与随机矩阵理论（RMT）预测的偏差有助于表征从近可积到混沌的过程，其方式有点类似于最近层间距分布。但是，EF 的统计数据揭示了更多属性，如下所述。 （i）在接近量子混沌的过程中，与大多数研究模型中的最近层间距分布相比，分量的分布表现出延迟特征。 (ii) 在量子混沌状态下，在具有经典对应物的模型中，分量的分布总是与 RMT 的预测显示出较小但显着的偏差，而在不具有经典对应物的模型中，这种偏差几乎可以忽略不计。 (iii) 在哈密顿矩阵具有清晰能带结构的模型中，EF尾部表现出与主体明显不同的统计行为，而对于不具有清晰能带结构的哈密顿矩阵，差异较小。
We study the statistical distribution of components in the non-perturbative parts of energy eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five models show that deviation of the distribution from the prediction of random matrix theory (RMT) is useful in characterizing the process from nearly-integrable to chaotic, in a way somewhat similar to the nearest-level-spacing distribution. But, the statistics of EFs reveals some more properties, as described below. (i) In the process of approaching quantum chaos, the distribution of components shows a delay feature compared with the nearest-level-spacing distribution in most of the models studied. (ii) In the quantum chaotic regime, the distribution of components always shows small but notable deviation from the prediction of RMT in models possessing classical counterparts, while, the deviation can be almost negligible in models not possessing classical counterparts. (iii) In models whose Hamiltonian matrices possess a clear band structure, tails of EFs show statistical behaviors obviously different from those in the main bodies, while, the difference is smaller for Hamiltonian matrices without a clear band structure.