伪二维晶格中的随机二聚体模型
Random dimer model in pseudo two-dimensional lattices
摘要：
在这项工作中，我们研究了相关和不相关的无序二维阵列中的长时间波输运。当一个分离的维度被应用到模型中，我们发现，预测的1D随机二聚体现象也出现在所谓的伪2D阵列。因此，在本征模的有效尺寸方面观察到阈值行为，以及在长时间动态中。为了观察到这种阈值行为，需要最小的系统尺寸，这在考虑可能的实验实现时非常重要。对于长时间的演化，我们发现对于短程相关晶格，观察到超扩散的长程输运，而对于完全不相关的二维输运无序，在局域长度内变得亚扩散，并且随机二元伪二维阵列显示局域化。
英文摘要：
In this work, we study long-time wave transport in correlated and uncorrelated disordered 2D arrays. When a separation of dimensions is applied to the model, we find that the predicted 1D random dimer phenomenology also appears in so-called pseudo-2D arrays. Therefore, a threshold behavior is observed in terms of the effective size for eigenmodes, as well as in long-time dynam- ics. For this threshold behavior to be observed a minimum system size is required, what is very important when considering a possible experimental realization. For the long-time evolution, we find that for short-range correlated lattices a super-diffusive long-range transport is observed, while for completely uncorrelated disorder in 2D transport becomes sub-diffusive within the localization length and random binary pseudo-2D arrays show localization.
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