arXiv subjects

Xianzhe Li

Publications and source records attributed to Xianzhe Li.

10 recordsLinked to original sources

arXiv2026

Dry Ten Martini Problem in the Subcritical Type I Regime

We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an application, we prove that, for every irrational frequency and every analytic potential, each subcritical Type I energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This confirms the conjecture of Ge--Jitomirskaya--You [GJY,You] in the subcritical regime.

math.SP↗

arXiv2026

Monotonicity, global symplectification and the stability of Dry Ten Martini Problem

We prove that, for every irrational frequency and every analytic Type I potential, each supercritical spectral energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This establishes the conjecture of Ge--Jitomirskaya--You \cite{GJY,You} in the supercritical regime. Consequently, the ``all gaps open'' property of the supercritical almost Mathieu operator persists under sufficiently small analytic perturbations. The main ingredient is a global symplectification of the center bundle that preserves quantitative monotonicity. This allows us to study gap opening through the center dynamics of the dual long-range operator, which has no natural Schrödinger form. We first establish the result for trigonometric polynomial potentials and then pass to general analytic potentials by controlling the dependence on the truncation dimension. The proof combines a discrete Hellmann--Feynman identity, dimension-free Aubry duality in weighted analytic norms, and a quantitative cone argument based on pre-monotonicity. These estimates ensure that the gaps survive in the analytic limit. Our results establish analytic stability of the Dry Ten Martini Problem in the supercritical regime and give a partial answer to a question of M. Shamis on the persistence of periodic spectral gaps.

math.DS↗

arXiv2026

Transfer Operators, Canonical Center Dynamics, and Spectral Applications for Long-Range Operators

We introduce an operator-theoretic framework for long-range operators over general dynamical systems with analytic hopping and small potential. By establishing a partially hyperbolic splitting on the fibered solution bundle, we define the Canonical Center Bundle (CCB) as the center subbundle of this splitting, which is shown to be globally trivial. The center bundle admits a representation via Riesz spectral projections of the transfer operator. Furthermore, we show that, in the local regime, the center bundle arising in this framework essentially coincides, in the sense of gap convergence, with the Intrinsic Center Bundles (ICB) obtained from finite-range approximations in \cite{GJ}. The partially hyperbolic structure thereby reduces the spectral problem to the center bundle, leading to a Johnson-type characterization of the spectrum in terms of the associated center cocycle. We then apply this framework to quasi-periodic Schrödinger operators with analytic hopping, large analytic potentials and Diophantine frequency. In this setting, the center cocycle is analytic and satisfies a Center Thouless formula. As consequences, we establish the absolute continuity of the integrated density of states (IDS), resolving a problem of Eliasson; prove quantitative Hölder continuity of the IDS, partially answering a question of You; and obtain Anderson localization for the original Schrödinger operators.

math.SP↗

arXiv2025

Intense and Tunable Multi-color Terahertz Radiation from Laser-Shaped Electron Beams

High-power multi-color terahertz (THz) radiation exhibits extraordinary scientific application prospects at various scientific frontiers, for its capacity to deliver THz excitation at multiple frequencies simultaneously. However, the generation of high-power multi-color THz radiation with tunable frequencies remains a challenge for existing techniques. Here, a technique by combining the multi-laser pulses frequency beating and coherent undulator amplification is proposed for generating high-power multi-color THz radiation with tunable frequency. Numerical simulations indicate that the proposed technique can produce multi-color THz radiation with three to six distinguished colors and a peak power up to hundreds of MW, and the temporally separated two-color pulses can also be produced by employing undulators with different resonance. Due to the intrinsic properties of the proposed technique, the THz frequencies, the color number and the frequency interval can be effectively controlled by simply adjusting the beating laser. This method paves the way for advanced application of THz pump-THz probe experiments for selective excitation of atomic multi-level systems and molecular fingerprint recognition.

physics.acc-ph↗

arXiv2025

Log-Hausdorff multifractality of the absolutely continuous spectral measure of the almost Mathieu operator

This paper focuses on the fractal characteristics of the absolutely continuous spectral measure of the subcritical almost Mathieu operator (AMO) and Diophantine frequency. In particular, we give a complete description of the (classical) multifractal spectrum and a finer description in the logarithmic gauge. The proof combines continued$-$fraction$/$metric Diophantine techniques and refined covering arguments. These results rigorously substantiate (and quantify in a refined gauge) the physicists' intuition that the absolutely continuous component of the spectrum is dominated by energies with trivial scaling index, while also exhibiting nontrivial exceptional sets which are negligible for classical Hausdorff measure but large at the logarithmic scale.

math-ph↗

arXiv2025

The fibered rotation number for ergodic symplectic cocycles and its applications: I. Gap Labelling Theorem

Let $ (Θ,T,μ) $ be an ergodic topological dynamical system. The fibered rotation number for cocycles in $ Θ\times \mathrm{SL}(2,\mathbb{R}) $, acting on $ Θ\times \mathbb{R}\mathbb{P}^1 $ is well-defined and has wide applications in the study of the spectral theory of Schrödinger operators. In this paper, we will provide its natural generalization for higher dimensional cocycles in $ Θ\times\mathrm{SP}(2m,\mathbb{R}) $ or $ Θ\times \mathrm{HSP}(2m,\mathbb{C}) $, where $ \mathrm{SP}(2m,\mathbb{R}) $ and $ \mathrm{HSP}(2m,\mathbb{C}) $ respectively refer to the $ 2m $-dimensional symplectic or Hermitian-symplectic matrices. As a corollary, we establish the equivalence between the integrated density of states for generalized Schrödinger operators and the fibered rotation number; and the Gap Labelling Theorem via the Schwartzman group, as expected from the one dimensional case [AS1983, JM1982].

math.DS↗

arXiv2024

Exact local distribution of the absolutely continuous spectral measure

It is well-established that the spectral measure for one-frequency Schrödinger operators with Diophantine frequencies exhibits optimal $1/2$-Hölder continuity within the absolutely continuous spectrum. This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified Hölder continuity of the spectral measure at subcritical energies.

math-ph↗

arXiv2022

Stability of Spectral Types of Quasi-Periodic Schrödinger Operators With Respect to Perturbations by Decaying Potentials

We consider perturbations of quasi-periodic Schrödinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the (almost) reducibility regime we prove that for perturbations with finite first moment, the essential spectrum remains purely absolutely continuous and the newly created discrete spectrum must be finite in each gap of the unperturbed spectrum. We also prove that for fixed phase, Anderson localization occurring for almost all frequencies in the regime of positive Lyapunov exponents is preserved under exponentially decaying perturbations.

math.SP↗

arXiv2022

Terahertz Receiver based on Room-Temperature Rydberg-Atoms

Realization of practical terahertz wireless communications still faces many challenges. The receiver with high sensitivity is important for THz wireless communications. Here we demonstrate a terahertz receiver based on the cesium Rydberg atoms in a room-temperature vapor cell. The minimum detectable THz electric field is calibrated. With this receiver, the phase-sensitive conversion of amplitude-modulated or frequency-modulated terahertz waves into optical signals is performed. The results show that the atomic receiver has many advantages due to its quantum properties. Especially, the long distance THz wireless communications is achievable using this receiver. Furthermore, the atomic receiver can be used in the THz wireless-to-optical link.

physics.atom-ph↗

arXiv2021

Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications

We establish a quantitative version of strong almost reducibility result for $\mathrm{sl}(2,\mathbb{R})$ quasi-periodic cocycle close to a constant in Gevrey class. We prove that, for the quasi-periodic Schrödinger operators with small Gevrey potentials, the length of spectral gaps decays sub-exponentially with respect to its labelling, the long range duality operator has pure point spectrum with sub-exponentially decaying eigenfunctions for almost all phases and the spectrum is an interval for discrete Schrödinger operator acting on $ \mathbb{Z}^d $ with small separable potentials. All these results are based on a refined KAM scheme, and thus are perturbative.

math.DS↗