Yunfeng Shi

activity

20172023

most citedAnderson localization for multi-frequency quasi-periodic operators on

Z^{d}

32 citations · 101 across the 20 of their papers we have counts for

collaborators

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8 papers · 1 filter

math.SP2020★ 5 cited

Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on $R^{d}$

Yunfeng Shi

In this paper we study on $L^{2} (R^{d})$ the quasi-periodic Schrödinger operator $H = - Δ + λV (x),$ where $V$ is a real analytic quasi-periodic function and $λ > 0$ . We first show t…

math.SP2020

A Multi-scale Analysis Proof of the Power-law Localization for Random Operators on $Z^{d}$

Yunfeng Shi

In this paper we give a multi-scale analysis proof of \textit{power-law} localization for random operators on $Z^{d}$ for \textit{arbitrary} $d \geq 1$ .

math.SP2019★ 3 cited

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…

math.SP2019★ 32 cited

Anderson localization for multi-frequency quasi-periodic operators on $Z^{d}$

Svetlana Jitomirskaya, Wencai Liu, Yunfeng Shi

We establish Anderson localization for general analytic $k$ -frequency quasi-periodic operators on $Z^{d}$ for \textit{arbitrary} $k, d$ .

math.SP2017

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 $H_{ε, ω} (x)$ : $(H_{ε, ω} (x) ψ)_{n} = ε k \in Z \sum W_{k} ψ_{n - k} + V (x + nω) ψ_{n},$ where $$\vecψ=\{\vecψ_n\}\in\ell^2(\…

math.SP2017★ 1 cited

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…

math.SP2017★ 1 cited

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,…

math.SP2017★ 18 cited

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…

Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on Rd

A Multi-scale Analysis Proof of the Power-law Localization for Random Operators on Zd

Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation

Anderson localization for multi-frequency quasi-periodic operators on Zd

Anderson localization for one-frequency quasi-periodic block operators with long-range interactions

Hölder continuity of the integrated density of states for Extended Harper's Model with Liouville frequency

Exponential Decay of the lengths of Spectral Gaps for Extended Harper's Model with Liouvillean Frequency

Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies

Absence of eigenvalues of analytic quasi-periodic Schrodinger operators on $R^{d}$

A Multi-scale Analysis Proof of the Power-law Localization for Random Operators on $Z^{d}$

Anderson localization for multi-frequency quasi-periodic operators on $Z^{d}$