93 citations · 292 across the 31 of their papers we have counts for
15 papers · 1 filter
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…
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…
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…
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…
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…
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…
Genericity of mode-locking for quasiperiodically forced circle maps
Jing Wang, Qi Zhou, Tobias Jäger
We show that a generic quasiperiodically forced circle homeomorphism is mode-locked: the rotation number in the fibres is rationally related to the rotation number in the base and…
Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications
Jiangong You, Qi Zhou
In this paper, we prove that any analytic quasi-periodic cocycle close to constant is the Poincaré map of an analytic quasi-periodic linear system close to constant. With this loca…