Zhiyan Zhao

activity

20152026

most citedAsymptotics of spectral gaps of quasi-periodic Schrödinger operators

32 citations · 91 across the 14 of their papers we have counts for

collaborators

14 papers

math-ph2026

Long-time stability for nonlinear Maryland models

Ruijie Cui, Zhiyan Zhao

For the $d -$ dimensional nonlinear Maryland model \begin{equation}\label{eq-abs} \ri\partial_t q_n=\tanπ(n\cdot\varpi+x)q_n+ε(Δq)_n+|q_n|^2q_n,\quad n\in{\Z^d}, \end{equation} with…

math.AP2026

Generalized Reducibility and Growth of Sobolev Norms

Zhenguo Liang, Zhiyan Zhao

We introduce the concept of {\it generalized reducibility}, which provides a flexible framework for analyzing the long-time behavior of solutions to quadratic quantum Hamiltonians.…

math-ph2025

Ballistic Transport for Discrete Multi-Dimensional Schrödinger Operators With Decaying Potential

David Damanik, Zhiyan Zhao

We consider the discrete Schrödinger operator $H = - Δ + V$ on $ℓ^{2} (Z^{d})$ with a decaying potential, in arbitrary lattice dimension $d \in N^{*}$ , where $Δ$ is the s…

math.AP2023★ 1 cited

Symplectic Normal Form and Growth of Sobolev Norm

Zhenguo Liang, Jiawen Luo, Zhiyan Zhao

For a class of reducible Hamiltonian partial differential equations (PDEs) with arbitrary spatial dimensions, quantified by a quadratic polynomial with time-dependent coefficients,…

math.AP2022★ 6 cited

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 $(x, - i \partial_{x})$ , we show its almost reducibility. The growth of Sobolev norms of so…

cs.CV2022★ 13 cited

FocalClick: Towards Practical Interactive Image Segmentation

Xi Chen, Zhiyan Zhao, Yilei Zhang +3

Interactive segmentation allows users to extract target masks by making positive/negative clicks. Although explored by many previous works, there is still a gap between academic ap…

math.CV2022

Geometry of hyperbolic Cauchy-Riemann singularities and KAM-like theory for holomorphic involutions

Laurent Stolovitch, Zhiyan Zhao

This article is concerned with the geometry of germs of real analytic surfaces in $(C^{2}, 0)$ having an isolated Cauchy-Riemann (CR) singularity at the origin. These are per…

math.AP2021★ 11 cited

Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation

Jiawen Luo, Zhenguo Liang, Zhiyan Zhao

We consider the one-dimensional quantum harmonic oscillator perturbed by a linear operator which is a polynomial of degree $2$ in $(x, - i \partial_{x})$ , with coefficients quasi-…

math.AP2020★ 2 cited

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 $C^{2}$ parametrized by $E \in I \subset R$ and quadratic on $x$ and $- i \partial_{x}$ w…

math-ph2019

Dispersive estimate for quasi-periodic Schrödinger operators on 1- $d$ lattices

Dario Bambusi, Zhiyan Zhao

Consider the one-dimensional discrete Schrödinger operator $H_{θ}$ : $(H_{θ} q)_{n} = - (q_{n + 1} + q_{n - 1}) + V (θ + nω) q_{n}, n \in Z,$ with $ω \in R^{d}$ Diophantine, and $V$ a real-ana…

math.DS2017★ 32 cited

Asymptotics of spectral gaps of quasi-periodic Schrödinger operators

Martin Leguil, Jiangong You, Zhiyan Zhao +1

For non-critical almost Mathieu operators with Diophantine frequency, we establish exponential asymptotics on the size of spectral gaps, and show that the spectrum is homogeneous.…

math.SP2016★ 12 cited

Ballistic Transport in One-Dimensional Quasi-Periodic Continuous Schrödinger Equation

Zhiyan Zhao

For the solution $q (t)$ to the one-dimensional continuous Schrödinger equation $i \partial_{t} q (x, t) = - \partial_{x}^{2} q (x, t) + V (ω x) q (x, t), x \in R,$ with $ω\in{\Bb…

math.DS2015★ 2 cited

Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators

Zhiyuan Zhang, Zhiyan Zhao

For the solution $u (t)$ to the discrete Schrödinger equation $i \frac{d}{d t} u_{n} (t) = - (u_{n + 1} (t) + u_{n - 1} (t)) + V (θ + n α) u_{n} (t), n \in Z,$ with $α\in\R\setminus\Q$ and $V\in…

math-ph2015★ 12 cited

Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schrödinger Equation

Zhiyan Zhao

For the solution $q (t) = (q_{n} (t))_{n \in Z}$ to one-dimensional discrete Schrödinger equation $i q ˙_{n} = - (q_{n + 1} + q_{n - 1}) + V (θ + nω) q_{n}, n \in Z,$ with $ω…

Long-time stability for nonlinear Maryland models

Generalized Reducibility and Growth of Sobolev Norms

Ballistic Transport for Discrete Multi-Dimensional Schrödinger Operators With Decaying Potential

Symplectic Normal Form and Growth of Sobolev Norm

Almost reducibility and oscillatory growth of Sobolev norms

FocalClick: Towards Practical Interactive Image Segmentation

Geometry of hyperbolic Cauchy-Riemann singularities and KAM-like theory for holomorphic involutions

Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation

1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms

Dispersive estimate for quasi-periodic Schrödinger operators on 1-d lattices

Asymptotics of spectral gaps of quasi-periodic Schrödinger operators

Ballistic Transport in One-Dimensional Quasi-Periodic Continuous Schrödinger Equation

Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators

Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schrödinger Equation

Dispersive estimate for quasi-periodic Schrödinger operators on 1- $d$ lattices