24 citations · 57 across the 15 of their papers we have counts for
5 papers · 1 filter
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…
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…