关于aOne-Dimensional格点传输的Bohigas猜想的反例
Counterexample to the Bohigas Conjecture for Transmission Through aOne-Dimensional Lattice
摘要：
研究了有限杂质存在下粒子在一维有限晶格中的共振传输。虽然这是一个经典可积的一维系统，没有混沌，但研究光谱的统计特性，如能级间距分布和光谱刚度，显示了量子混沌特征。使用一个无量纲的参数，反映了状态本地化的程度，我们演示了如何从正则到混沌的过渡是受状态本地化。共振位置的计算使用Wigner-Smith时间延迟和Siegert状态的方法，这是在很好的协议。我们的结果证明了一维量子混沌的存在，这是对Bohigas-Giannoni-Schmit猜想的反例。
英文摘要：
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 quantum chaos signatures. Using a dimensionless parameter that reflects the degree of state localization, we demonstrate how the transition from regularity to chaos is affected by state localization. The resonance positions are calculated using both the Wigner-Smithtime-delay and a Siegert state method, which are in good agreement. Our results give evidence for the existence of quantum chaos in one dimension which is a counter-example to the Bohigas-Giannoni-Schmit conjecture.
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