93 citations · 292 across the 31 of their papers we have counts for
32 papers
Gaussian rigidity for infinite exchangeable sequences
Yushu Zheng, Qi Zhou
We prove a Gaussian rigidity theorem for infinite exchangeable sequences of real-valued random variables: the joint Gaussianity of a single pair of entries already forces the entir…
Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
Christopher Cedzich, Jake Fillman, Long Li +2
We investigate the symmetries of so-called generalized extended CMV matrices. It is well-documented that problems involving reflection symmetries of standard extended CMV matrices…
Non-Self-Adjoint Quasi-periodic Operators with complex spectrum
Zhenfu Wang, Jiangong You, Qi Zhou
We give a precise and complete description on the spectrum for a class of non-self-adjoint quasi-periodic operators acting on which contains the Sarnak's mod…
Multiplicative Jensen's formula and quantitative global theory of one-frequency Schrödinger operators
Lingrui Ge, Svetlana Jitomirskaya, Jiangong You +1
We introduce the concept of dual Lyapunov exponents, leading to a multiplicative version of the classical Jensen's formula for one-frequency analytic Schrödinger cocycles. This for…
Dry Ten Martini Problem in the non-critical case
Artur Avila, Jiangong You, Qi Zhou
We solve the Dry Ten Martini Problem in the non-critical case, i.e., all possible spectral gaps are open for almost Mathieu operators with .
Absolute continuity of the integrated density of states in the localized regime
Jing Wang, Xu Xu, Jiangong You +1
We establish the absolute continuity of the integrated density of states (IDS) for quasi-periodic Schrödinger operators with a large trigonometric potential and Diophantine frequen…
Winding number, density of states and acceleration
Xueyin Wang, Zhenfu Wang, Jiangong You +1
Winding number and density of states are two fundamental physical quantities for non-self-adjoint quasi-periodic Schrödinger operators, which reflect the asymptotic distribution of…
Stability of Spectral Types of Quasi-Periodic Schrödinger Operators With Respect to Perturbations by Decaying Potentials
David Damanik, Xianzhe Li, Jiangong You +1
We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under whi…
Almost reducibility and oscillatory growth of Sobolev norms
Zhenguo Liang, Zhiyan Zhao, Qi Zhou
For 1D quantum harmonic oscillator perturbed by a time quasi-periodic quadratic form of , we show its almost reducibility. The growth of Sobolev norms of so…
Isospectrum of non-self-adjoint almost-periodic Schrodinger operators
Xueyin Wang, Jiangong You, Qi Zhou
For non-self-adjoint almost-periodic Schrödinger operators, a criterion is given to guarantee that they have both the same spectrum and same Lyapunov exponents with the discrete fr…
Almost-periodic ground state of the non-self-adjoint Jacobi operator and its applications
Xing Liang, Honngze Wang, Qi Zhou
We study the ground states of the one-dimensional non-self-adjoint Jacobi operators in the almost periodic media by using the method of dynamical systems. We show the existence of…
Nevanlinna class, Dirichlet series and Szegö's problem
Kunyu Guo, Jiaqi Ni, Qi Zhou
This paper is associated with Nevanlinna class, Dirichlet series and Szegö's problem in infinitely many variables. As we will see, there is a natural connection between these topic…
Cantor Spectrum for CMV Matrices With Almost Periodic Verblunsky Coefficients
Long Li, David Damanik, Qi Zhou
We consider extended CMV matrices with analytic quasi-periodic Verblunsky coefficients with Diophantine frequency vector in the perturbatively small coupling constant regime and pr…
Quantitative almost reducibility and Möbius disjointness for analytic quasiperiodic Schrodinger cocycles
Wen Huang, Jing Wang, Zhiren Wang +1
Sarnak's Möbius disjointness conjecture states that Möbius function is disjoint to any zero entropy dynamics. We prove that Möbius disjointness conjecture holds for one-frequency a…
Exact mobility edges for 1D quasiperiodic models
Yongjian Wang, Xu Xia, Jiangong You +2
Mobility edges (ME), i.e. critical energies which separate absolutely continuous spectrum and purely point spectrum, is an important issue in quantum physics. So far there are two…
On the abominable properties of the almost Mathieu operator with well approximated frequencies
Artur Avila, Yoram Last, Mira Shamis +1
We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensi…
Traveling fronts for Fisher-KPP lattice equations in almost periodic media
Xing Liang, Hongze Wang, Qi Zhou +1
This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the…
Absolutely Continuous Spectrum for CMV Matrices With Small Quasi-Periodic Verblunsky Coefficients
Long Li, David Damanik, Qi Zhou
We consider standard and extended CMV matrices with small quasi-periodic Verblunsky coefficients and show that on their essential spectrum, all spectral measures are purely absolut…
Global rigidity for ultra-differentiable quasiperiodic cocycles and its spectral applications
Hongyu Cheng, Lingrui Ge, Jiangong You +1
For quasiperiodic Schrödinger operators with one-frequency analytic potentials, from dynamical systems side, it has been proved that the corresponding quasiperiodic Schrödinger coc…
Anosov-Katok constructions for quasi-periodic cocycles
Nikolaos Karaliolios, Xu Xu, Qi Zhou
We prove that if the frequency of the quasi-periodic cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1…
Absolutely Continuous Spectrum of Multifrequency Quasiperiodic Schrödinger operator
Xuanji Hou, Jing Wang, Qi Zhou
In this paper, we prove that for any -frequency analytic quasiperiodic Schrödinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the co…
1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms
Zhenguo Liang, Zhiyan Zhao, Qi Zhou
For a family of 1-d quantum harmonic oscillator with a perturbation which is parametrized by and quadratic on and w…
Exponential Dynamical Localization: Criterion and Applications
Lingrui Ge, Jiangong You, Qi Zhou
We give a criterion for exponential dynamical localization in expectation (EDL) for ergodic families of operators acting on . As applications, we prove EDL for a clas…
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…