Point spectrum for quasi-periodic long range operators

Jiangong You, Shiwen Zhang, Qi Zhou

Type: Article

Publication Date: 2015-01-06

Citations: 7

DOI: https://doi.org/10.4171/jst/85

Abstract

We generalize Gordon type argument to quasi-periodic operators with finite range interaction and prove that these operators have no point spectrum when the rational approximation rate of the base frequency is relatively large. We also show that, for any irrational frequency, there are operators with infinite range interaction possessing point spectrum. is is a new phenomenon which can not happen in the finite range interaction case.

Locations

Journal of Spectral Theory - View - PDF

Similar Works

Action	Title	Year	Authors
+	Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation	2019	Yunfeng Shi
+	Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach	2022	Yunfeng Shi
+	On the Point Spectrum of a Non-Self-Adjoint Quasiperiodic Operator	2024	D. I. Borisov Alexander Fedotov
+ PDF Chat	Localization for Almost-Periodic Operators with Power-law Long-range Hopping: A Nash-Moser Iteration Type Reducibility Approach	2023	Yunfeng Shi
+	Localization for a class of discrete long-range quasi-periodic operators	2022	Yunfeng Shi Li Wen
+ PDF Chat	A finite range operator with a quasi-periodic potential	1996	Steve Surace
+	Schrödinger operators with point interactions and short range expansions	1984	Sergio Albeverio Raphaël Høegh-Krohn
+	Research on quasi-weakly almost periodic point	2024	Yingcui Zhao Lidong Wang
+	Non-Self-Adjoint Quasi-periodic Operators with complex spectrum	2023	Zhenfu Wang Jiangong You Qi Zhou
+	Reducibility of finitely differentiable quasi-periodic cocycles and its spectral applications	2017	Ao Cai Lingrui Ge
+	A note on quasi-weakly almost periodic point	2015	Qi Yan Jian Dong Yin Tao Wang
+	Non-Quasi-Periodic Normal Form Theory	2023	Gabriella Pinzari
+	Quasiperiodic Version of Gordon’s Theorem	2023	Sergey Bolotin Dmitry Treschev
+	Anderson localization for Schrödinger operators with monotone potentials over circle homeomorphisms	2024	Jiranan Kerdboon Xiaowen Zhu
+ PDF Chat	Non-Self-Adjoint Quasi-periodic Operators with complex spectrum	2024	Zhenfu Wang Jiangong You Qi Zhou
+	Methods of KAM-theory for long-range quasi-periodic operators on ℤ v . Pure point spectrum	1993	Victor Chulaevsky E. I. Dinaburg
+	Anderson localization for one-frequency quasi-periodic block operators with long-range interactions	2017	Wenwen Jian Yunfeng Shi Xiaoping Yuan
+	Dynamical localization for finitely differentiable quasi-periodic long-range operators	2025	Yuan Shan
+ PDF Chat	Bethe-Sommerfeld conjecture for periodic operators with strong perturbations	2010	Leonid Parnovski Alexander V. Sobolev
+	Almost Periodic Function	2010	Математика

Works That Cite This (7)

Action	Title	Year	Authors
+	Stability for Cauchy problem of first order linear PDEs on $ \mathbb{T}^m $ with forced frequency possessing finite uniform Diophantine exponent	2024	Xinyu Guan Nan Kang
+ PDF Chat	Interior inverse problem for global conservative multipeakon solutions of the Camassa-Holm equation	2024	Tao Liu Kang Lyu
+	Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,R)$ cocycles	2020	Nikolaos Karaliolios Xu Xu Qi Zhou
+	Absence of eigenvalues for quasiperiodic Schrödinger type operators	2019	Jiahao Xu Xin Zhao
+	Stoker's Problem for Quasi-periodically Forced Reversible Systems with Multidimensional Liouvillean Frequency	2020	Xiaodan Xu Wen Si Jianguo Si
+ PDF Chat	Interior Inverse Problem for Global Conservative Multipeakon Solutions of the Camassa-Holm Equation	2024	Tao Liu Kang Lyu
+	Anosov–Katok Constructions for Quasi-Periodic $$\textrm{SL}(2,{{\mathbb {R}}})$$ Cocycles	2022	Nikolaos Karaliolios Xu Xu Qi Zhou

Works Cited by This (8)

Action	Title	Year	Authors
+	Absolutely continuous spectrum for 1D quasiperiodic operators	2002	Jean Bourgain Svetlana Jitomirskaya
+	Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems	2012	Xuanji Hou Jiangong You
+ PDF Chat	Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications	2013	Jiangong You Qi Zhou
+ PDF Chat	Singular continuous spectrum for a class of almost periodic Jacobi matrices	1982	J. E. Avron Barry Simon
+ PDF Chat	A nonperturbative Eliasson's reducibility theorem	2005	Joaquim Puig
+ PDF Chat	Almost localization and almost reducibility	2009	Artur Avila Svetlana Jitomirskaya
+	Almost reducibility and absolute continuity I	2010	Artur Avila
+	A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies	2010	Artur Avila Bassam Fayad Raphaël Krikorian