5 papers
Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on
Yunfeng Shi, W. -M. Wang
We establish large sets of Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on , thus extending Anderson localization from the linear (…
Green's function estimates for quasi-periodic operators on with power-law long-range hopping
Yunfeng Shi, Li Wen
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on with power-law long-range hopping and analytic cosine type poten…
Localization for Lipschitz monotone quasi-periodic Schrödinger operators on via Rellich functions analysis
Hongyi Cao, Yunfeng Shi, Zhifei Zhang
We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on with bounded or unbounded Lipsc…
On the spectrum of quasi-periodic Schrödinger operators on with -cosine type potentials
Hongyi Cao, Yunfeng Shi, Zhifei Zhang
In this paper, we establish the Anderson localization, strong dynamical localization and the -Hölder continuity of the integrated density of states (IDS) for some mul…
Diophantine estimates on shifts of trigonometric polynomials on
Yunfeng Shi, W. -M. Wang
We establish Diophantine type estimates on shifts of trigonometric polynomials on the torus , as well as that of their square roots. These estimates arise from the sp…