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Extension of Floquet's theory to nonlinear quasiperiodic differential equations

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Science China Mathematics 2005年第12期48卷 1670-1682页

作者： WU Hao LI Weigu School of Mathematical Sciences Peking UniversityBeijing 100871China School of Mathematical SciencesPeking UniversityBeijing 100871China

In this paper, we consider the following autonomous system of differential equations: x = Ax + f(x,θ), θ = ω, where θ∈Rm, ω = (ω1,…,ωm) ∈ Rm, x ∈ Rn, A ∈ Rn×n is a constant matrix and is hyperbolic, f is a C∞ function in both variables and 2π-periodic in each component of the vector e which satisfies f = O(||x||2) as x → 0. We study the normal form of this system and prove that under some proper conditions this system can be transformed to an autonomous system: x = Ax + g(x), θ = ω. Additionally, the proof of this paper naturally implies the extension of Chen's theory in the quasi-periodic case.

关键词： quasiperiodic system,normal form.

Absence of eigenvalues for quasiperiodic Schrodinger type operators

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Frontiers of Mathematics in China 2019年第3期14卷 645-659页

作者： Jiahao XU Xin ZHAO Department of Mathematical Sciences Nanjing University Nanjing 210093 China

We obtain the matrix-valued Schrodinger-type operators [Hα,θ] with Lipschitz potentials having no eigenvalues on the set {E : L ( E )<δ)C,d(α,θ),where δ is an explicit function depending on the sampling function... 详细信息

关键词： quasiperiodic Schrodinger type operators absence of eigenvalues singular continuous spectrum

Effective Reducibility of a Class of Linear Differential Equations with quasiperiodic Coefficients

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Acta Mathematica Sinica,English Series 2004年第3期20卷 525-532页

作者： RenZiYANG JunXiangXU DepartmentofMathematics SoutheastUniversityNanjing210018P.R.China

In this paper we consider the effective reducibility of the following linear differential equation: , where A is a constant matrix, Q(t,?) is quasiperiodic in t, and ? is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to , where R* is exponentially small in ?.

关键词： Linear differential equations Effective reducibility quasiperiodic

Invariable mobility edge in a quasiperiodic lattice

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Chinese Physics B 2022年第2期31卷 534-537页

作者： Tong Liu Shujie Cheng Rui Zhang Rongrong Ruan Houxun Jiang School of Science Nanjing University of Posts and TelecommunicationsNanjing 210003China Department of Physics Zhejiang Normal UniversityJinhua 321004China

We analytically and numerically study a 1 D tight-binding model with tunable incommensurate *** utilize the self-dual relation to obtain the critical energy,namely,the mobility ***,we analytically demonstrate that this critical energy is a constant independent of strength of *** we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal *** numerical results are in excellent agreement with the analytical ***,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.

关键词： Anderson localization quasiperiodic mobility edge multifractal

Wave-vector-dependent Tunneling Transmission Characteristics in Periodic and quasiperiodic Semiconductor Superlattices

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Tsinghua Science and Technology 2000年第2期5卷 121-127页

作者：郭永王浩顾秉林 Department of Physics Tsinghua University Beijing 100084 China

Wave vector dependent tunneling transmission in periodic and quasiperiodic semiconductor superlattices is investigated while the coupling between longitudinal and transverse momentums is taken into account. It is shown that: (1) there exists a transition from tunneling through effective multiple barriers to transport above effective multiple wells with increasing transverse wave number k xy ;(2) the transmission spectrum for periodic superlattices exhibits resonant domains separated by nonresonant gaps, and the resonance splitting is regular;(3) the transmission spectrum for quasiperiodic superlattices exhibits complicated oscillations and selective suppressions, both singlet and doublet resonances exist in the considered quasiperiodic systems, and there exist more doublet resonances in high order generations of the Thue Morse sequence; (4) complete resonant tunneling can occur in the quasiperiodic superlattice.

关键词： tunneling superlattice periodic quasiperiodic

Real eigenvalues determined by recursion of eigenstates

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Chinese Physics B 2024年第3期33卷 196-200页

作者：刘通王友国 School of Science Nanjing University of Posts and TelecommunicationsNanjing 210003China

Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time *** the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific ***,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian *** this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of ***,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.

关键词： real eigenvalues non-Hermitian quasiperiodic

Aubry–Mather Sets for Relativistic Oscillators with Anharmonic Potentials

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Acta Mathematica Sinica,English Series 2017年第3期33卷 439-448页

作者： Guang Hua SHI College of Mathematics and Computer Science Hu'nan Normal University Hu'nan 410006 P. R. China

In this paper, by the Aubry-Mather theory, it is proved that there are many periodic solutions and usual or generalized quasiperiodic solutions for relativistic oscillator with anharmonic potentials models d/dt（x/√1... 详细信息

关键词： Aubry-Mather sets quasiperiodic relativistic

Inner edge of accretion disks in low mass X-ray binaries

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Science China Mathematics 1995年第9期38卷 1117-1126页

作者：李向东汪珍如 Department of Astronomy Nanjing University Nanjing 210093 China

The magnitude of the inner edge of accretion disks in low mass X-ray binaries is controversial in theoretical considerations and observations. Using the inner boundary conditions of accretion disks the inner disk radius has been calculated by taking into account the effect of feedback radiation and the deviation of disk rotation from Keplerian. Results have been applied to the observations and possible interpretations have been proposed for the X-ray spectra and quasiperiodic oscillations.

关键词： low mass X-ray binaries accretion disks X-ray spectra quasiperiodic oscillations.

Spectral Structure and Gap-Labeling Properties for a New Class of One-Dimensional Quasilattices

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Chinese Physics Letters 1992年第11期9卷 609-612页

作者： HUANG Xiuqing LIU Youyan Department of Physics South China University of TechnologyGuangzhou 510641 Nanchang Army college Nanchang 330103 International Center for Materials Physics Academia SinicaShenyang 110015

A new class of 1D quasiperiodic lattices,for which the substitution rules are B→BA,and A→BAB,has been studied in several *** high-dimensional projection method for obtaining the quasilattice is presented.A multifractral spectral behavior and gap fabeling properties have been found,which display the perfect quasiperiodicity of the studied model.

关键词： lattices quasiperiodic substitution