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Yingte Sun

Publications and source records attributed to Yingte Sun.

7 recordsLinked to original sources
arXiv2026

How the Angle of Static Field Affects the Spectrum of Lattice Schrodinger Operator on $\mathbb{Z}^2$

The spectral properties of the discrete Schrodinger operator on a two-dimensional lattice under uniform static fields are critically governed by the field direction: for angles parameterized by irrational frequencies, the operator is exponentially localized, and for a subset of such angles with asymptotically full Lebesgue measure, this localization persists under a given logarithmically decaying perturbation potential.

math.SP↗
arXiv2026

Localized state for nonlinear disordered stark model

In this paper, we consider the following nonlinear disordered Stark model: $${\bf i}\partial_tu_n+\delta(u_{n+1}+u_{n-1})+nu_n+v_nu_n+\epsilon |u_n|^{2}u_n=0,\quad n\in\mathbb{Z}.$$ By employing the diagonalization of the associated linear operators and the KAM theory for nonlinear Hamiltonian systems, we establish that for parameters $\delta$ and $\varepsilon$ in a reasonable range, and for most realization of random variables $v=\{v_n\}_{n \in \mathbb{Z}}$, there exist time quasi-periodic and spatially localized states that exhibit arbitrary power-law spatial decay.

math.DS↗
arXiv2022

The stability of Sobolev norms for the linear wave equation with unbounded perturbations

In this paper, we prove that the Sobolev norm of solutions of the linear wave equation with unbounded perturbations of order one stay bounded for the all time. The main proof is based on the KAM reducibility of the linear wave equation. To the best of our knowledge, this is the first reducibility result of the linear wave equation with general quasi-periodic unbounded potentials on the torus.

math.AP↗
arXiv2018

Reducibility for wave equations of finitely smooth potential with periodic boundary conditions

In the present paper, the reducibility is derived for the wave equations with finitely smooth and time-quasi-periodic potential subjects to periodic boundary conditions. More exactly, the linear wave equation $u_{tt}-u_{xx}+Mu+\varepsilon (V_0(\omega t)u_{xx}+V(\omega t, x)u)=0,\;x\in \mathbb{R}/2\pi \mathbb{Z}$ can be reduced to a linear Hamiltonian system of a constant coefficient operator which is of pure imaginary point spectrum set, where $V$ is finitely smooth in $(t, x)$, quasi-periodic in time $t$ with Diophantine frequency $\omega\in \mathbb{R}^{n},$ and $V_0$ is finitely smooth and quasi-periodic in time $t$ with Diophantine frequency $\omega\in \mathbb{R}^{n},$ Moreover, it is proved that the corresponding wave operator possesses the property of pure point spectra and zero Lyapunov exponent.

math.DS↗