Transport exponents of Sturmian Hamiltonians
Transport exponents of Sturmian Hamiltonians
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Sturmian 哈密顿量的传输指数
DOI：
10.1016/j.jfa.2015.05.018
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发表时间：
2015
影响因子：
1.7
通讯作者：
Damanik D.
中科院分区：
文献类型：
--
作者：
Damanik David D.;Gorodetski Anton S.;Liu Qinghui;Qu Yanhui;Damanik D.
我们考虑Sturmian势的离散薛定谔算子，并研究与之相关的输运指数。在适当的频率假设下，我们建立了上输运指数的上界和下界。作为这些界限的应用，我们确定了大的耦合渐近常数型频率的上输运指数。我们还从上面的Lebesgue典型频率一致的大耦合渐近界。这些结果的一个特殊后果是，对于大多数频率的恒定类型，运输是快于勒贝格几乎每一个频率。我们还显示了所有的耦合常数，通用频率，和合适的相位准弹道输运。
We consider discrete Schrödinger operators with Sturmian potentials and study the transport exponents associated with them. Under suitable assumptions on the frequency, we establish upper and lower bounds for the upper transport exponents. As an application of these bounds, we identify the large coupling asymptotics of the upper transport exponents for frequencies of constant type. We also bound the large coupling asymptotics uniformly from above for Lebesgue-typical frequency. A particular consequence of these results is that for most frequencies of constant type, transport is faster than for Lebesgue almost every frequency. We also show quasi-ballistic transport for all coupling constants, generic frequencies, and suitable phases.