5 citations · 23 across the 15 of their papers we have counts for
17 papers
The Dry Ten Martini Problem for subcritical Type I operators
Lingrui Ge
We supply the details of the subcritical dry Ten Martini statement announced in [6, Remark 1.3]: for every irrational frequency, every subcritical Type I energy with resonant rotat…
The Robust Ten Martini Problem
Lingrui Ge, Svetlana Jitomirskaya, Jiangong You
We solve the robust ten martini problem: Cantor spectrum with no arithmetic restriction on the irrational frequency for Type I analytic one-frequency quasiperiodic Schrodinger oper…
Intrinsic Symplectic Structure and Sharp Arithmetic Universality
Lingrui Ge, Svetlana Jitomirskaya
We show that formal eigenvalue equations of analytic one-frequency Schröd-inger operators admit intrinsic analytic $Sp(2k,\C)$ structures, where is the T-acceleration in g…
Sharp Spectral Gaps, Arithmetic Localization, and Reducibility via Resonance Analys
Lingrui Ge, Jiangong You, Qi Zhou
This paper establishes several sharp spectral results for analytic quasiperiodic Schrodinger operators. Key contributions include: (1) exact exponential decay rates for spectral ga…
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…
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…
Hofstadter butterflies and metal/insulator transitions for moiré heterostructures
Simon Becker, Lingrui Ge, Jens Wittsten
We consider a tight-binding model recently introduced by Timmel and Mele for strained moiré heterostructures. We consider two honeycomb lattices to which layer antisymmetric shear…
Stability of the non-critical spectral properties I: arithmetic absolute continuity of the integrated density of states
Lingrui Ge, Svetlana Jitomirskaya, Xin Zhao
We prove absolute continuity of the integrated density of states for frequency-independent analytic perturbations of the non-critical almost Mathieu operator under arithmetic condi…
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…
Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
Lingrui Ge, Ilya Kachkovskiy
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schrödinger operators with smooth potentials demonstrate ballistic motion on the set of energies…
The precise regularity of the Lyapunov exponent for Cos-type quasiperiodic Schrödinger cocycles with large couplings
Jiahao Xu, Lingrui Ge, Yiqian Wang
In this paper, we study the regularity of the Lyapunov exponent for quasiperiodic Schrödinger cocycles with cos-type potentials, large coupling constants, and a fixed Diophan…
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…
Reducibility of finitely differentiable quasi-periodic cocycles and its spectral applications
Ao Cai, Lingrui Ge
In this paper, we prove the generic version of Cantor spectrum for quasi-periodic Schrödinger operators with finitely smooth and small potentials, and we also show pure point spect…