32 citations · 101 across the 20 of their papers we have counts for
20 papers
Diagonalization in a quantum kicked rotor model with non-analytic potential
Yunfeng Shi, Li Wen
In this paper we study the lattice quasi-periodic operators with power-law long-range hopping and meromorphic monotone potentials, and diagonalize the operators via a Nash-Moser it…
Anderson localized states for the quasi-periodic nonlinear wave equation on
Yunfeng Shi, W. -M. Wang
We establish large sets of Anderson localized states for the quasi-periodic nonlinear wave equation on , thus extending nonlinear Anderson localization from the random…
Localization for random coupled harmonic oscillators on
Hongzi Cong, Yunfeng Shi, Zhihan Zhang
In this paper we consider the localization properties of coupled harmonic oscillators in random media. Each of these oscillators is restricted to the lattice . We sho…
Localization and Regularity of the Integrated Density of States for Schrödinger Operators on with -cosine Like Quasi-periodic Potential
Hongyi Cao, Yunfeng Shi, Zhifei Zhang
In this paper, we study the multidimensional lattice Schrödinger operators with -cosine like quasi-periodic (QP) potential. We establish quantitative Green's function estimate…
Quantitative Green's Function Estimates for Lattice Quasi-periodic Schrödinger Operators
Hongyi Cao, Yunfeng Shi, Zhifei Zhang
In this paper, we establish quantitative Green's function estimates for some higher dimensional lattice quasi-periodic (QP) Schrödinger operators. The resonances in the estimates c…
Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach
Yunfeng Shi
In this paper we develop a Nash-Moser iteration type reducibility approach to prove the (inverse) localization for some -dimensional discrete almost-periodic operators with powe…
Diffusion bound for the nonlinear Anderson model
Hongzi Cong, Yunfeng Shi
In this paper, we prove the power-law in time upper bound for the diffusion of a 1D discrete nonlinear Anderson model. We remove completely the decaying condition restricted on the…
Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on
Yunfeng Shi
In this paper we study on the quasi-periodic Schrödinger operator where is a real analytic quasi-periodic function and . We first show t…
Long-time Anderson Localization for the Nonlinear Schrodinger Equation Revisited
Hongzi Cong, Yunfeng Shi, Zhifei Zhang
In this paper, we confirm the conjecture of Wang and Zhang (J. Stat. Phys. 134 (5-6): 953--968, 2009) in a long time scale, i.e., the displacement of the wavefront for nonline…
A Multi-scale Analysis Proof of the Power-law Localization for Random Operators on
Yunfeng Shi
In this paper we give a multi-scale analysis proof of \textit{power-law} localization for random operators on for \textit{arbitrary} .
On linear stability of KAM tori via the Craig-Wayne-Bourgain method
Xiaolong He, Jia Shi, Yunfeng Shi +1
In this paper, we prove the Melnikov's persistency theorem by combining the traditional Kolmogorov-Arnold-Moser (KAM) technique and the Craig-Wayne-Bourgain (CWB) method. The aim o…
Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation
Yunfeng Shi
In this paper, we study the multi-frequency quasi-periodic operator with a Gevrey type perturbation. We first establish the large deviation theorem (LDT) for the multi-dimensional…
Anderson localization for multi-frequency quasi-periodic operators on
Svetlana Jitomirskaya, Wencai Liu, Yunfeng Shi
We establish Anderson localization for general analytic -frequency quasi-periodic operators on for \textit{arbitrary} .
On the existence of full dimensional KAM torus for nonlinear Schrödinger equation
Hongzi Cong, Lufang Mi, Yunfeng Shi +1
In this paper, we study the following nonlinear Schrödinger equation \begin{eqnarray}\label{maineq0} \textbf{i}u_{t}-u_{xx}+V*u+εf(x)|u|^4u=0,\ x\in\mathbb{T}=\mathbb{R}/2π\mathbb{…
Analytic solutions of nonlinear elliptic equations on rectangular tori
Yunfeng Shi
In this paper, we consider the nonlinear elliptic equations on rectangular tori. Using methods in the study of KAM theory and Anderson localization, we prove that these equations a…
Anderson localization for one-frequency quasi-periodic block operators with long-range interactions
Wenwen Jian, Yunfeng Shi, Xiaoping Yuan
In this paper, we study the quasi-periodic operators : where $$\vecψ=\{\vecψ_n\}\in\ell^2(\…
Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency
Wenwen Jian, Yunfeng Shi
In this paper, we study the non-self-dual extended Harper's model with a Liouville frequency. Based on the work of \cite{SY}, we show that the integrated density of states (IDS for…
Exponential Decay of the lengths of Spectral Gaps for Extended Harper's Model with Liouvillean Frequency
Yunfeng Shi, Xiaoping Yuan
In this paper, we study the non-self dual extended Harper's model with Liouvillean frequency. By establishing quantitative reducibility results together with the averaging method,…
Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies
Wencai Liu, Yunfeng Shi
We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schrödinger operators with Liouville frequencies decays exponentially. As an application, we obtain the…
The Stability of Full Dimensional KAM tori for Nonlinear Schrödinger equation
Hongzi Cong, Jianjun Liu, Yunfeng Shi +1
In this paper, it is proved that the full dimensional invariant tori obtained by Bourgain [J. Funct. Anal., \textbf{229} (2005), no. 1, 62-94.] is stable in a very long time for 1D…