Phase-Averaged Transport¶for Quasi-Periodic Hamiltonians
Phase-Averaged Transport¶for Quasi-Periodic Hamiltonians
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准周期哈密顿量的相位平均输运¶
DOI：
10.1007/s002200200642
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
H. Schulz
中科院分区：
文献类型：
--
作者：
J. Bellissard;I. Guarneri;H. Schulz
对于一类由旋转代数的协变表示定义的离散准周期薛定谔算子，证明了相位平均输运的态密度的多重分形维数的下界。这一结果是在不定参数条件下建立的。相关类的运营商的区别是不变性相对于对称自同构的旋转代数。它包括关键的哈珀（几乎马蒂厄）运营商。作为副产品，我们给出了相干态Weyl-Heisenberg-Gabor格点框架问题的一个新的解。
For a class of discrete quasi-periodic Schrödinger operators defined by covariant representations of the rotation algebra, a lower bound on phase-averaged transport in terms of the multifractal dimensions of the density of states is proven. This result is established under a Diophantine condition on the incommensuration parameter. The relevant class of operators is distinguished by invariance with respect to symmetry automorphisms of the rotation algebra. It includes the critical Harper (almost-Mathieu) operator. As a by-product, a new solution of the frame problem associated with Weyl–Heisenberg–Gabor lattices of coherent states is given.