准周期链中的波包动力学、遍历性和局部化
Wave Packet Dynamics, Ergodicity, and Localization in Quasiperiodic Chains
摘要：
本文报道了一类由两类弱耦合团簇组成的准周期链中的波包动力学。通过返回概率和均方位移研究了动力学。波包显示出在一个逐步的快速膨胀过程中的异常扩散，随后是有限的波包宽度的时间间隔。应用微扰理论，其中耦合参数v被视为微扰，系统的本征态的性质进行了研究，并与链的结构。结果表明，非定域态的出现，只有在足够高的订单的微扰展开。此外，我们将这些结果与数值对角化得到的精确解进行比较。这表明，当v>0时，本征态分布在整个链上，而在极限v->0时，遍历性被打破，本征态只分布在同一类型的簇中，这与v=0时的平凡局域化形成对比。由于这种遍历性破坏，波包动力学在杂质的存在下显著改变，从而提供了控制其长期动力学的可能性。
英文摘要：
In this paper, we report results for the wave packet dynamics in a class of quasiperiodic chains consisting of two types of weakly coupled clusters. The dynamics are studied by means of the return probability and the mean square displacement. The wave packets show anomalous diffusion in a stepwise process of fast expansion followed by time intervals of confined wave packet width. Applying perturbation theory, where the coupling parameter v is treated as perturbation, the properties of the eigenstates of the system are investigated and related to the structure of the chains. The results show the appearance of non-localized states only in sufficiently high orders of the perturbation expansions. Further, we compare these results to the exact solutions obtained by numerical diagonalization. This shows that eigenstates spread across the entire chain for v>0, while in the limit v->0 ergodicity is broken and eigenstates only spread across clusters of the same type, in contradistinction to trivial localization for v=0. Caused by this ergodicity breaking, the wave packet dynamics change significantly in the presence of an impurity offering the possibility to control its long-term dynamics.
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