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Xueyin Wang

Publications and source records attributed to Xueyin Wang.

15 recordsLinked to original sources
arXiv2026

Arithmetic $k$-Polynomial Dynamical Localization for $k$ Power-Law Quasi-Periodic Long-Range Operators on $\ell^2(\mathbb{Z}^d)$

We establish a criterion of arithmetic $k$-polynomial spectral localization and $k$-polynomial dynamical localization in expectation for quasi-periodic long-range operators on $\ell^2(\mathbb{Z}^{d})$ with power-law hopping based on the quantitative $C^{k}$-reducibility of the dual Schrödinger cocycle. As the application, we prove both localization properties for power-law long-range perturbations of the Almost Mathieu Operators with sufficiently large couplings and Diophantine frequencies.

math.DS↗
arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive Hölder class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-Hölder continuity of the integrated density of states for the associated quasiperiodic Schrödinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Sharp Logarithmic Quantum Dynamics for Quasiperiodic Schrödinger Operators

Dynamical localization requires all position moments of a quantum wavepacket to remain bounded in time, but for quasiperiodic Schrödinger operators such bounds are generally not uniform in phase. In the positive Lyapunov exponent regime, the best known phase-uniform estimates instead grow on a logarithmic scale. We prove that both the logarithmic scale and the dependence on the moment order are sharp for a class of one-frequency quasiperiodic Schrödinger operators with even potentials. Our main ingredient is a reflective version of semi-uniformly localized eigenfunctions, adapted to the two localization centers forced by a completely resonant phase, from which we obtain matching logarithmic lower bounds along sequences of times.

math-ph↗
arXiv2025

PhotoDoodle: Learning Artistic Image Editing from Few-Shot Pairwise Data

We introduce PhotoDoodle, a novel image editing framework designed to facilitate photo doodling by enabling artists to overlay decorative elements onto photographs. Photo doodling is challenging because the inserted elements must appear seamlessly integrated with the background, requiring realistic blending, perspective alignment, and contextual coherence. Additionally, the background must be preserved without distortion, and the artist's unique style must be captured efficiently from limited training data. These requirements are not addressed by previous methods that primarily focus on global style transfer or regional inpainting. The proposed method, PhotoDoodle, employs a two-stage training strategy. Initially, we train a general-purpose image editing model, OmniEditor, using large-scale data. Subsequently, we fine-tune this model with EditLoRA using a small, artist-curated dataset of before-and-after image pairs to capture distinct editing styles and techniques. To enhance consistency in the generated results, we introduce a positional encoding reuse mechanism. Additionally, we release a PhotoDoodle dataset featuring six high-quality styles. Extensive experiments demonstrate the advanced performance and robustness of our method in customized image editing, opening new possibilities for artistic creation.

cs.CV↗
arXiv2023

An Experimental Study of Satisfaction Response: Evaluation of Online Collaborative Learning

On the one hand, a growing amount of research discusses support for improving online collaborative learning quality, and many indicators are focused to assess its success. On the other hand, thinkLets for designing reputable and valuable collaborative processes have been developed for more than ten years. However, few studies try to apply thinkLets to online collaborative learning. This paper introduces thinkLets to online collaborative learning and experimentally tests its effectiveness with participants' responses on their satisfaction. Yield Shift Theory (YST), a causal theory explaining inner satisfaction, is adopted. In the experiment, 113 students from Universities in Beijing, China are chosen as a sample. They were divided into two groups, collaborating online in a simulated class. Then, YST in student groups under online collaborative learning is validated, a comparison study of online collaborative learning with and without thinkLets is implemented, and the satisfaction response of participants are analyzed. As a result of this comparison, YST is proved applicable in this context, and satisfaction is higher in online collaborative learning with thinkLets.

cs.HC↗
arXiv2023

Spectrum of Hatano-Nelson model with strictly ergodic potentials

We provide a precise formula for the spectrum of the Hatano-Nelson model with strictly ergodic potentials in terms of its Lyapunov exponent. As applications, one clearly observes the real-complex spectrum transition. Moreover, if the Lyapunov exponent is continuous, the spectrum of the Hatano-Nelson model in $\ell^{2}(\mathbb{Z})$ can be approximated by the spectrum of its finite-interval truncation with periodic boundary conditions. Both of these results are strikingly different from the Hatano-Nelson model with random potentials \cite{Dav01A, Dav01, Dav02}.

math.SP↗
arXiv2023

Winding number, density of states and acceleration

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 zeros of the characteristic determinants of the truncated operators under Dirichlet boundary condition, with respect to complexified phase and the energy respectively. We will prove that the winding number is in fact Avila's acceleration and it is also closely related to the density of states by a generalized Thouless formula for non-self-adjoint Schrödinger operators and Avila's global theory.

math-ph↗
arXiv2022

Isospectrum of non-self-adjoint almost-periodic Schrodinger operators

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 free Laplacian. As a byproduct, we show that the Moser-Pöschel argument for opening gaps may not be valid for non-self-adjoint operators.

math.DS↗
arXiv2020

Polynomial decay of the gap length for C^k quasi-periodic Schrodinger operators and spectral application

For the quasi-periodic Schrödinger operators in the local perturbative regime where the frequency is Diophantine and the potential is $C^k$ sufficiently small depending on the Diophantine constants, we prove that the length of the corresponding spectral gap has a polynomial decay upper bound with respect to its label. This is based on a refined quantitative reducibility theorem for $C^k$ quasi-periodic ${\rm SL}(2,\mathbb{R})$ cocycles, and also based on the Moser-Pöschel argument for the related Schrödinger cocycles. As an application, we are able to show the homogeneity of the spectrum.

math.DS↗