Observation of Wigner-Dyson level statistics in a classically integrable system
Observation of Wigner-Dyson level statistics in a classically integrable system
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经典可积系统中维格纳-戴森能级统计的观察
DOI：
10.1103/physreve.103.062211
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发表时间：
2021
影响因子：
2.4
通讯作者：
Greene, Chris H.
中科院分区：
文献类型：
--
作者：
Elkamshishy, Ahmed A.;Greene, Chris H.
在存在有限数量杂质的情况下，研究了粒子通过一维有限晶格传输的共振。尽管这是一个经典可积且无混沌的一维系统，但研究谱的统计特性（例如能级间距分布和谱刚度）显示出与混沌系统获得的统计相同的统计数据。使用反映状态局部化程度的无量纲参数，我们演示了状态局部化如何影响从泊松级统计到维格纳-戴森统计的转变。使用 Wigner-Smith 时间延迟和 Siegert 态方法计算共振位置，两者吻合良好。我们的结果表明，当定位长度从泊松分布演变为维格纳-戴森分布时，级别统计数据对定位长度的依赖性。
Resonances in particle transmission through a 1D finite lattice are studied in the presence of a finite number of impurities. Although this is a one-dimensional system that is classically integrable and has no chaos, studying the statistical properties of the spectrum such as the level spacing distribution and the spectral rigidity shows the same statistics as the one obtained for chaotic systems. Using a dimensionless parameter that reflects the degree of state localization, we demonstrate how the transition from Poisson-level statistics to the Wigner-Dyson is affected by state localization. The resonance positions are calculated using both the Wigner-Smith time delay and a Siegert state method, which are in good agreement. Our results show the dependence of the level statistics on the localization length as it evolves from a Poisson distribution to Wigner-Dyson.