On the Ambarzumyan's theorem for the Quasi-periodic Problem
Alp Arslan Kıraç
当位势$q$上没有任何附加条件时，我们得到了Sturm-Liouville算子$L_{t}(q)$具有$q\in L^{1}[0,1]$和拟周期边界条件$t\in [0,2π)$的经典Ambarzumyan定理.
We obtain the classical Ambarzumyan's theorem for the Sturm-Liouville operators $L_{t}(q)$ with $q\in L^{1}[0,1]$ and quasi-periodic boundary conditions, $t\in [0,2π)$, when there is not any additional condition on the potential $q$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We extend the classical Ambarzumyan's theorem to the quasi-periodic boundary value problems by using only a part knowledge of one spectrum. We also weaken slightly the Yurko's conditions on the first eigenvalue.
A further note on the inverse nodal problem and Ambarzumyan problem for the p-Laplacian
本文将前人关于p-Laplacian反节点问题和Ambarzumyan问题的一些结果推广到周期或反周期边界条件和L^1位势。
Absolutely continuous spectrum for quasi-periodic Schrödinger operators
证明了任意维数的拟周期薛定谔算子具有一定的绝对连续谱。
Finite and full scale localization for the multi-frequency quasi-periodic CMV matrices
研究多频准周期CMV矩阵的有限和全尺度局域化方法，提出与Goldstein等人关于多频准周期Schrödinger算子局域化结果相对应的CMV矩阵结果。
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 homogeneity of the spectrum.
The spectrum of the multi-frequency quasi-periodic CMV matrices contains intervals
本文研究多频拟周期CMV矩阵的谱结构，在正Lyapunov指数和Diophantine条件下证明其谱在单位圆上包含区间。
Scattering Theory for Jacobi Operators with Quasi-Periodic Background
我们发展了雅可比算子的正、逆散射理论，雅可比算子是准周期有限能隙算子的短程微扰。我们证明了变换算子的存在性，研究了它们的性质，导出了相应的Gel'fand-Levitan-Marchenko方程，并找到了唯一确定扰动算子的最小散射数据.
Trace Formulas in Connection with Scattering Theory for Quasi-Periodic Background
利用Krein谱移理论研究了拟周期有限间隙算子的迹族扰动Jacobi算子的迹公式。特别是，我们建立了保守量的解决方案的户田层次在这个类。
On Quasi-periodic Differential Pencils with Jump Conditions Inside the Interval
研究了有限区间上非自伴的二阶微分束在非分离的准周期边界条件和跳跃条件下的解。我们建立了谱特征的性质，并研究了从谱数据中恢复算子的逆谱问题。对于这个反问题，我们证明了相应的唯一性定理，并提供了一个算法来构造它的解决方案。
In this paper, we study block Jacobi operators on $\mathbb{Z}$ with quasi-periodic meromorphic potential. We prove the non-perturbative Anderson localization for such operators in the large coupling regime.
Construction of finite differentiable quasi-periodic Schrödinger operators with cantor spectrum
本文提出显式构造具有康托尔谱的 $C^k$ 拟周期薛定谔算子的方法，并给出谱间隙大小的多项式渐近估计。
Anderson Localization for Time Quasi Periodic Random Schödinger and Wave Operators
通过证明相关的准能量算子具有纯点谱，证明了在大无序、大概率和大测度丢番图频率下，$\Bbb Z^d$中的Anderson定域在定域时间准周期扰动下是{ \it稳定}的.主要的工具是Fröhlich-Spencer机制的随机分量和Bourgain-Goldstein-Schlag机制的准周期分量。这个问题的提法是由非线性薛定谔方程的安德森本地化问题的动机。
In this paper, we study quasi-periodic CMV matrices with Verblunsky coefficients given by the skew-shift. We prove the positivity of Lyapunov exponents and Anderson localization for most frequencies, which establish the analogous results of one-dimensional Schrödinger operators proved by Bourgain, Goldstein and Schlag.
Asymptotics for the Eigenvalues of the Harmonic Oscillator with a Quasi-Periodic Perturbation
我们考虑H+V形式的算子，其中H是一维谐振子，V是零阶伪微分算子，在适当的意义下是准周期的（例如，可以将V乘以周期函数）。本文证明了H+V的特征值具有渐近性：λ n（H+V）=λ n（H）+W（\sqrt n）n^{-1/4}+O（n^{-1/2} \ln（n））as \to + \infty，其中W是一个可用V明确定义的准周期函数.
We establish Anderson localization for general analytic $k$-frequency quasi-periodic operators on $\mathbb{Z}^d$ for \textit{arbitrary} $k,d$.
Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator Under Time Quasi- Periodic Perturbations
我们证明了$1-d$量子谐振子在空间定域、时间准周期扰动下对正测度丢番图频率是稳定的。这证明了Enss-Veselic在他们1983年的论文\cite{EV}中提出的一个猜想。本文的动机也来自于相应的非线性方程的拟周期解的构造。
We discover that the distribution of (frequency and phase) resonances plays a role in determining the spectral type of supercritical quasi-periodic Schrödinger operators. In particular, we disprove the second spectral transition line conjecture of Jitomirskaya in the early 1990s.
We consider standard and extended CMV matrices with small quasi-periodic Verblunsky coefficients and show that on their essential spectrum, all spectral measures are purely absolutely continuous. This answers a question of Barry Simon from 2005.
Ballistic Transport for Schrödinger Operators with Quasi-periodic Potentials
该研究证明了任意维度d>1下，带一般准周期势的薛定谔算子存在弹道输运，推进了相关算子谱理论研究。
We consider CMV matrices, both standard and extended, with analytic quasi-periodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a result Bourgain and Goldstein proved for discrete one-dimensional Schrödinger operators. We also prove a similar result for quantum walks on the integer lattice with suitable analytic quasi-periodic coins.
Quantum Dynamical Bounds for Quasi-Periodic Operators with Liouville Frequencies
针对具有刘维尔频率的拟周期薛定谔算子，结合克罗内克序列的半代数偏差估计与适配刘维尔情形的定量格林函数估计，建立了量子动力学上界。
We consider a one-frequency, quasi-periodic, block Jacobi operator, whose blocks are generic matrix-valued analytic functions. We establish Anderson localization for this type of operator under the assumption that the coupling constant is large enough but independent of the frequency. This generalizes a result of J. Bourgain and S. Jitomirskaya on localization for band lattice, quasi-periodic Schroedinger operators.
Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators
我们证明了具有解析系数的准周期Jacobi算子在正李雅普诺夫指数和强丢番图条件下积分态密度的Hölder连续性。特别地，当系数是三角多项式时，我们用系数的次数来表示霍德尔指数。
We show that a generic quasi-periodic Schrödinger operator in $L^2(\mathbb{R})$ has purely singular spectrum. That is, for any minimal translation flow on a finite-dimensional torus, there is a residual set of continuous sampling functions such that for each of these sampling functions, the Schrödinger operator with the resulting potential has empty absolutely continuous spectrum.
Anderson localization of long-range quasi-periodic operators via Dynamical Rigidity
本文通过动力学刚性论证，证明了长程准周期算子在大三角函数势和迪奥菲antine频率下的安德森局域化。
We consider the quasi-periodic Schrödinger operator with the non-degenerate Gevrey potential for the Diophantine frequency. We prove that if the coupling number of the potential is large, then the spectrum is homogeneous.
Mixed spectral types for the one frequency discrete quasi-periodic Schrödinger operator
考虑一族单频离散解析拟周期Schr在[Bjer]中出现的Odinger操作符。我们证明了这个族提供了一个例子，绝对连续和点谱共存的一些参数，以及绝对连续和奇异连续谱共存的一些其他参数。
In this paper we study on $L^2(\mathbb{R}^d)$ the quasi-periodic Schrödinger operator $H=-Δ+ λV(x),$ where $V$ is a real analytic quasi-periodic function and $λ>0$. We first show that $H$ has no eigenvalues in \textit{low energy region}. We also provide in \textit{low energy region} the new phase transition parameter, i.e. the competition between the strength of coupling and the length for frequencies.
On the singular spectrum for adiabatic quasi-periodic Schrodinger operators on the real line
本文研究了实直线上一类拟周期Schrodinger算子族在绝热极限下的谱性质。我们假设绝热等能曲线沿动量方向延伸。在这种情况发生的能量区间，我们得到了一个渐近公式的李雅普诺夫指数，并表明，频谱是纯奇异的。
For non-critical almost Mathieu operators with Diophantine frequency, we establish exponential asymptotics on the size of spectral gaps, and show that the spectrum is homogeneous. We also prove the homogeneity of the spectrum for Schödinger operators with (measure-theoretically) typical quasi-periodic analytic potentials and fixed strong Diophantine frequency. As applications, we show the discrete version of Deift's conjecture \cite{Deift, Deift17} for subcritical analytic quasi-periodic initial data and solve a series of open problems of Damanik-Goldstein et al \cite{BDGL, DGL1, dgsv, Go} and…
We consider one-dimensional quasi-periodic Schrödinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates which lead to optimal Hölder continuity of the Lyapunov exponents and the integrated density of states, in both small Lyapunov exponent and large coupling regimes. Our results cover all the Diophantine frequencies and some Liouville frequencies.
Solution of the Sturm-Liouville and the Korteweg-de-Vries equations with periodic and quasi-periodic parameters using theory of vessels
利用Sturm-Liouville（SL）方程的Backlund变换，利用SL容器理论证明了具有周期和拟周期位势q（x）的SL方程-y”（x）+q（x）y（x）= s^2y（x）解的存在性.本文拟周期是指周期可积函数的有限和。对于离散Levinson数集s=sn，n-自然数，一般s的解是根据满足SL方程的解zn（x）显式构造的，初始条件zn（0）=0，zn '（0）=1.相应容器的tau函数tau（x）通过公式q（x）=-2（ln（tau（x）"实现给定的势。我们还证明了一个模拟的逆散射定理在这种设置。利用“KdV演化容器”的概念，构造了Korteweg-de-Vries（KdV）方程q't =-3/2qq 'x + 1/4 q' xxx的解，该解在t=0时与给定的（周期或准周期）势相一致.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。