论文标题
环域的状态，径向大周期性和卡利树上的量子蝴蝶
Ring-localized states, radial aperiodicity and quantum butterflies on a Cayley tree
论文作者
论文摘要
我们基于真实空间分解方案提出了一种分析方法，以提取在Cayley Tree Fractal网络中固定的局部激励集的确切特征值。在一个紧密的结合方案中，我们利用上述方法来审查网络确定性变形的效果，首先是通过层次分布在最近的邻居跳跃积分值中的层次分布，然后通过径向aubry Andre andre harper harper quasiperiodic模型。随着发电指数的增加，膨胀环的较少树结构寄托在外围特征状态上，从最外面的环向大部分样品散布，类似于森林火的蔓延，照亮了一组可预测的地点，并留下了其余的未注入。可以精确地设计振幅信封的渗透深度。准碘调制产生迄今未报告的量子蝴蝶，通过计算本征态的反参与率和多重分析分析，已进一步研究了量子蝴蝶。最后讨论了该方案对光子分形波导网络的适用性。
We present an analytical method, based on a real space decimation scheme, to extract the exact eigenvalues of a macroscopically large set of pinned localized excitations in a Cayley tree fractal network. Within a tight binding scheme we exploit the above method to scrutinize the effect of a deterministic deformation of the network, first through a hierarchical distribution in the values of the nearest neighbor hopping integrals, and then through a radial Aubry Andre Harper quasiperiodic modulation. With increasing generation index, the inflating loop less tree structure hosts pinned eigenstates on the peripheral sites that spread from the outermost rings into the bulk of the sample, resembling the spread of a forest fire, lighting up a predictable set of sites and leaving the rest unignited. The penetration depth of the envelope of amplitudes can be precisely engineered. The quasiperiodic modulation yields hitherto unreported quantum butterflies, which have further been investigated by calculating the inverse participation ratio for the eigenstates, and a multifractal analysis. The applicability of the scheme to photonic fractal waveguide networks is discussed at the end.
