244 citations · 716 across the 28 of their papers we have counts for
28 papers
Discontinuity of Lyapunov exponent in spaces of quasiperiodic cocycles: Smoothness vs Arithmetic
Jinhao Liang, Kai Tao, Jiangong You
We construct examples of discontinuity of Lyapunov exponent in the spaces of quasiperiodic -cocycles for fixed irrational frequencies. Especially, we prov…
Global structure of the spectrum of periodic Non-hermitian Jacobi operators
Hui Lu, Jiangong You
The global structure of the spectrum of periodic non-Hermitian Jacobi operators is described by the discriminant and its stationary points. We also give necessary and sufficient co…
Kotani theory, Puig's argument, and stability of The Ten Martini Problem
Lingrui Ge, Svetlana Jitomirskaya, Jiangong You
We solve the ten martini problem (Cantor spectrum with no condition on irrational frequencies, previously only established for the almost Mathieu) for a large class of one-frequenc…
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…
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…
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…
Arithmetic version of anderson localization for quasiperiodic Schrödinger operators with even cosine type potentials
Lingrui Ge, Jiangong You, Xin Zhao
We propose a new method to prove Anderson localization for quasiperiodic Schrödinger operators and apply it to the quasiperiodic model considered by Sinai and Fröhlich-Spencer-Witt…
Transition space for the continuity of the Lyapunov exponent of quasiperiodic Schrödinger cocycles
Lingrui Ge, Yiqian Wang, Jiangong You +1
We construct discontinuous point of the Lyapunov exponent of quasiperiodic Schrödinger cocycles in the Gevrey space with . In contrast, the Lyapunov exponent has been…
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…
Hölder regularity of the integrated density of states for quasi-periodic long-range operators on
Lingrui Ge, Jiangong You, Xin Zhao
We prove the Hölder continuity of the integrated density of states for a class of quasi-periodic long-range operators on with large trigonometric polynomial potentia…
One dimensional quasiperiodic mosaic lattice with exact mobility edges
Yucheng Wang, Xu Xia, Long Zhang +5
The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiod…
Arithmetic version of Anderson localization via reducibility
Lingrui Ge, Jiangong You
The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given b…
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…
Hölder continuity of Lyapunov exponent for a family of smooth Schrödinger cocycles
Jinhao Liang, Yiqian Wang, Jiangong You
We prove the Hölder continuity of the Lyapunov exponent for quasi-periodic Schrödinger cocycles with a cos-type potential and any fixed Liouvillean frequency, provided the co…
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.…
Quasi-periodic solutions of NLS with Liouvillean Frequency
Xindong Xu, Jiangong You, Qi Zhou
Quasi-periodic solutions with Liouvillean frequency of forced nonlinear Schrödinger equation are constructed. This is based on an infinite dimensional KAM theory for Liouvillean fr…
Sharp Holder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles
Ao Cai, Claire Chavaudret, Jiangong You +1
We show that if the base frequency is Diophantine, then the Lyapunov exponent of a quasi-periodic cocycle is -Hölder continuous in the almost reduci…
Linearization of quasiperiodically forced circle flow beyond Brjuno condition
Raphael Krikorian, Jing Wang, Jiangong You +1
We prove that an analytic quasiperiodically forced circle flow with a not super-Liouvillean base frequency and which is close enough to some constant rotation is rotat…
Sharp Phase transitions for the almost Mathieu operator
Artur Avila, Jiangong You, Qi Zhou
It is known that the spectral type of the almost Mathieu operator depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the fr…