24 citations · 46 across the 11 of their papers we have counts for
12 papers
The Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian
Qinghui Liu, Yiran Lv
In 2015, Liu, Qu (Commun. Math. Phys., Vol. 338) show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian admits a positive lower bound independent of the co…
The Hausdorff dimension of spectrum of a class of gerneralized Thue-Morse Hamiltonians
Qinghui Liu, Zhiyi Tang
We study a class of Schrödinger operators with generalized Thue-Morse potential that generated by the substitution , on two symbol alphabet $Σ=…
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…
A note on minimum linear arrangement for BC graphs
Xiaofang Jiang, Qinghui Liu, Natarajan Parthiban +1
A linear arrangement is a labeling or a numbering or a linear ordering of the vertices of a graph. In this paper we solve the minimum linear arrangement problem for bijective conne…
"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.
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…
Gibbs-like measure for spectrum of a class of one-dimensional Schrödinger operator with Sturm potentials
Shen Fan, Qing-Hui Liu, Zhi-Ying Wen
Let be an irrational, and the continued fraction expansion of . Let be the one-dimensional Schrödinger operator with Sturm potential of f…