24 citations · 57 across the 15 of their papers we have counts for
15 papers
Cantor spectrum for multidimensional quasi-periodic Schrödinger operators
Bernard Helffer, Qinghui Liu, Yanhui Qu +1
In this paper, we investigate the spectrum of a class of multidimensional quasi-periodic Schrödinger operators that exhibit a Cantor spectrum, which provides a resolution to a ques…
Almost sure dimensional properties for the spectrum and the density of states of Sturmian Hamiltonians
Jie Cao, Yanhui Qu
In this paper, we find a full Lebesgue measure set of frequencies $\check \II\subset [0,1]\setminus \Q$ such that for any $(α,λ)\in \check \II\times [24,\infty)$, the Hausdorff and…
The spectrum of period-doubling Hamiltonian
Qinghui Liu, Yanhui Qu, Xiao Yao
In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than , where is the Golden number; there e…
Positive Hausdorff dimensional spectrum for the critical almost Mathieu operator
Bernard Helffer, Qinghui Liu, Yanhui Qu +1
We show that there exists a dense set of frequencies with positive Hausdorff dimension for which the Hausdorff dimension of the spectrum of the critical almost Mathieu operator is…
Continuous spectrum for a class of smooth mixing Schrödinger operators
Bassam Fayad, Yanhui Qu
We give the first example of a smooth volume preserving mixing dynamical system such that the discrete Schrödinger operators on the line defined with a potential generated by this…
Exact-dimensional property of density of states measure of Sturm Hamiltonian
Yanhui Qu
For frequency of bounded type and coupling , we show that the density of states measure $\NN_{α,λ}$ of the related Sturm Hamiltonian is exact upper and lower dimensional,…
"Mixed spectral nature" of Thue--Morse Hamiltonian
Qinghui Liu, Yanhui Qu, Xiao Yao
We find three dense subsets and of the spectrum of the Thue-Morse Hamiltonian, such that each energy in is extended, each energy in is pseudo-…
Spectral Properties of Schrödinger Operators With Pattern Sturmian Potentials
David Damanik, Qing-Hui Liu, Yan-Hui Qu
We consider discrete Schrödinger operators with pattern Sturmian potentials. This class of potentials strictly contains the class of Sturmian potentials, for which the spectral pro…
Transport Exponents of Sturmian Hamiltonians
David Damanik, Anton Gorodetski, Qing-Hui Liu +1
We consider discrete Schrödinger operators with Sturmian potentials and study the transport exponents associated with them. Under suitable assumptions on the frequency, we establis…
On the Hausdorff dimension of the spectrum of Thue-Morse Hamiltonian
Qinghui Liu, Yanhui Qu
We show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian has a common positive lower bound for all coupling.
The spectral properties of the strongly coupled Sturm Hamiltonian of eventually constant type
Yanhui Qu
We study the spectral properties of the Sturm Hamiltolian of eventually constant type, which includes the Fibonacci Hamiltonian. Let be the Hausdorff dimension of the spectrum.…
Iteration of polynomial pair under Thue-Morse dynamic
Qinghui Liu, Yanhui Qu
We study the behavior of a polynomial sequence which is defined by iterating a polynomial pair under Thue-Morse dynamic. We show that in suitable sense, the sequence will behave li…
The fractal dimensions of the spectrum of Sturm Hamiltonian
Qinghui Liu, Yanhui Qu, Zhiying Wen
Let be irrational and be the continued fraction expansion of . Let be the Sturm Hamiltonian with frequency and coupling , $Σ_{α…
Localized asymptotic behavior for almost additive potentials
Julien Barral, Yan-Hui Qu
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost additive continuous potentials on a topologically mixing subshift o…
Multifractal analysis and localized asymptotic behavior for almost additive potentials
Julien Barral, Yan-Hui Qu
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost-additive continuous potentials on a topologically mixing subshift o…