The Spectrum of Period-Doubling Hamiltonian
The Spectrum of Period-Doubling Hamiltonian
复制标题
倍周期哈密顿量的谱
DOI：
10.1007/s00220-022-04417-7
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发表时间：
2021
影响因子：
2.4
通讯作者：
Xiao Yao
中科院分区：
文献类型：
--
作者：
Qinghui Liu;Yanhui Qu;Xiao Yao
本文证明了：倍周期哈密顿量谱的Hausdorff维数大于$log alpha/log 4$，其中$alpha$是Golden数;存在一个稠密的不可数谱子集，使得对于这个集合中的每个能量，相关的迹轨道是无界的，这与Carvalho最近的一个结果相反（Nonlinearity 33，2020）;我们给出了间隙结构和光谱的差距标记的完整表征。所有这些结果的内在编码的频谱，我们在本文中构建的后果。
In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than $log alpha/log 4$, where $alpha$ is the Golden number; there exists a dense uncountable subset of the spectrum such that for each energy in this set, the related trace orbit is unbounded, which is in contrast with a recent result of Carvalho (Nonlinearity 33, 2020); we give a complete characterization for the structure of gaps and the gap labelling of the spectrum. All of these results are consequences of an intrinsic coding of the spectrum we construct in this paper.