发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - Spectral Theory最新文献

筛选
英文 中文
Lieb-Thirring inequalities for the shifted Coulomb Hamiltonian 移动库仑哈密顿的李卜-蒂林不等式
arXiv - MATH - Spectral Theory Pub Date : 2024-09-02 DOI: arxiv-2409.01291
Thiago Carvalho Corso, Timo Weidl, Zhuoyao Zeng
{"title":"Lieb-Thirring inequalities for the shifted Coulomb Hamiltonian","authors":"Thiago Carvalho Corso, Timo Weidl, Zhuoyao Zeng","doi":"arxiv-2409.01291","DOIUrl":"https://doi.org/arxiv-2409.01291","url":null,"abstract":"In this paper we prove sharp Lieb-Thirring (LT) inequalities for the family\u0000of shifted Coulomb Hamiltonians. More precisely, we prove the classical LT\u0000inequalities with the semi-classical constant for this family of operators in\u0000any dimension $dgeqslant 3$ and any $gamma geqslant 1$. We also prove that\u0000the semi-classical constant is never optimal for the Cwikel-Lieb-Rozenblum\u0000(CLR) inequalities for this family of operators in any dimension. In this case,\u0000we characterize the optimal constant as the minimum of a finite set and provide\u0000an asymptotic expansion as the dimension grows. Using the same method to prove\u0000the CLR inequalities for Coulomb, we obtain more information about the\u0000conjectured optimal constant in the CLR inequality for arbitrary potentials.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inducing countable Lebesgue spectrum 诱导可数勒贝格谱
arXiv - MATH - Spectral Theory Pub Date : 2024-08-31 DOI: arxiv-2409.00396
Fatna Abdedou, Bassam Fayad, Jean-Paul Thouvenot
{"title":"Inducing countable Lebesgue spectrum","authors":"Fatna Abdedou, Bassam Fayad, Jean-Paul Thouvenot","doi":"arxiv-2409.00396","DOIUrl":"https://doi.org/arxiv-2409.00396","url":null,"abstract":"We show that every ergodic dynamical system induces a system with pure\u0000Lebesgue spectrum of infinite multiplicity.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tail Bounds for Functions of Weighted Tensor Sums Derived from Random Walks on Riemannian Manifolds 从黎曼曼曲面上的随机漫步推导出的加权张量和函数的尾界
arXiv - MATH - Spectral Theory Pub Date : 2024-08-31 DOI: arxiv-2409.00542
Shih-Yu Chang
{"title":"Tail Bounds for Functions of Weighted Tensor Sums Derived from Random Walks on Riemannian Manifolds","authors":"Shih-Yu Chang","doi":"arxiv-2409.00542","DOIUrl":"https://doi.org/arxiv-2409.00542","url":null,"abstract":"This paper presents significant advancements in tensor analysis and the study\u0000of random walks on manifolds. It introduces new tensor inequalities derived\u0000using the Mond-Pecaric method, which enriches the existing mathematical tools\u0000for tensor analysis. This method, developed by mathematicians Mond and Pecaric,\u0000is a powerful technique for establishing inequalities in linear operators and\u0000matrices, using functional analysis and operator theory principles. The paper\u0000also proposes novel lower and upper bounds for estimating column sums of\u0000transition matrices based on their spectral information, which is critical for\u0000understanding random walk behavior. Additionally, it derives bounds for the\u0000right tail of weighted tensor sums derived from random walks on manifolds,\u0000utilizing the spectrum of the Laplace-Beltrami operator over the underlying\u0000manifolds and new tensor inequalities to enhance the understanding of these\u0000complex mathematical structures.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixed Steklov-Neumann problem: asymptotic analysis and applications to diffusion-controlled reactions 斯特克洛夫-诺伊曼混合问题：渐近分析及其在扩散控制反应中的应用
arXiv - MATH - Spectral Theory Pub Date : 2024-08-30 DOI: arxiv-2409.00213
Denis S. Grebenkov
{"title":"Mixed Steklov-Neumann problem: asymptotic analysis and applications to diffusion-controlled reactions","authors":"Denis S. Grebenkov","doi":"arxiv-2409.00213","DOIUrl":"https://doi.org/arxiv-2409.00213","url":null,"abstract":"Many first-passage processes in complex media and related\u0000diffusion-controlled reactions can be described by means of eigenfunctions of\u0000the mixed Steklov-Neumann problem. In this paper, we investigate this spectral\u0000problem in a common setting when a small target or escape window (with Steklov\u0000condition) is located on the reflecting boundary (with Neumann condition). We\u0000start by inspecting two basic settings: an arc-shaped target on the boundary of\u0000a disk and a spherical-cap-shaped target on the boundary of a ball. We\u0000construct the explicit kernel of an integral operator that determines the\u0000eigenvalues and eigenfunctions and deduce their asymptotic behavior in the\u0000small-target limit. By relating the limiting kernel to an appropriate\u0000Dirichlet-to-Neumann operator, we extend these asymptotic results to other\u0000bounded domains with smooth boundaries. A straightforward application to\u0000first-passage processes is presented; in particular, we revisit the\u0000small-target behavior of the mean first-reaction time on perfectly or partially\u0000reactive targets, as well as for more sophisticated surface reactions that\u0000extend the conventional narrow escape problem.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the intertwining map between Coulomb and hyperbolic scattering 论库仑散射与双曲散射之间的交织映射
arXiv - MATH - Spectral Theory Pub Date : 2024-08-29 DOI: arxiv-2408.16248
Nicholas Lohr
{"title":"On the intertwining map between Coulomb and hyperbolic scattering","authors":"Nicholas Lohr","doi":"arxiv-2408.16248","DOIUrl":"https://doi.org/arxiv-2408.16248","url":null,"abstract":"We construct a unitary operator between Hilbert spaces of generalized\u0000eigenfunctions of Coulomb operators and the Laplace-Beltrami operator of\u0000hyperbolic space that intertwines their respective Poisson operators on\u0000$L^2(mathbb{S}^{d-1})$. The constructed operator generalizes Fock's unitary\u0000transformation, originally defined between the discrete spectra of the\u0000attractive Coulomb operator and the Laplace-Beltrami operator on the sphere, to\u0000the setting of continuous spectra. Among other connections, this map explains\u0000why the scattering matrices are the same in these two different settings, and\u0000it also provides an explicit formula for the Poisson operator of the Coulomb\u0000Hamiltonian.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation 具有半约束变化势的准周期算子的锐算脱域问题
arXiv - MATH - Spectral Theory Pub Date : 2024-08-29 DOI: arxiv-2408.16935
Svetlana Jitomirskaya, Ilya Kachkovskiy
{"title":"Sharp arithmetic delocalization for quasiperiodic operators with potentials of semi-bounded variation","authors":"Svetlana Jitomirskaya, Ilya Kachkovskiy","doi":"arxiv-2408.16935","DOIUrl":"https://doi.org/arxiv-2408.16935","url":null,"abstract":"We obtain the sharp arithmetic Gordon's theorem: that is, absence of\u0000eigenvalues on the set of energies with Lyapunov exponent bounded by the\u0000exponential rate of approximation of frequency by the rationals, for a large\u0000class of one-dimensional quasiperiodic Schr\"odinger operators, with no\u0000(modulus of) continuity required. The class includes all unbounded monotone\u0000potentials with finite Lyapunov exponents and all potentials of bounded\u0000variation. The main tool is a new uniform upper bound on iterates of cocycles\u0000of bounded variation.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral analysis of a coupled bending-torsion beam energy harvester: asymptotic results 耦合弯曲扭转梁能量收集器的频谱分析：渐近结果
arXiv - MATH - Spectral Theory Pub Date : 2024-08-28 DOI: arxiv-2408.15635
Chris Vales
{"title":"Spectral analysis of a coupled bending-torsion beam energy harvester: asymptotic results","authors":"Chris Vales","doi":"arxiv-2408.15635","DOIUrl":"https://doi.org/arxiv-2408.15635","url":null,"abstract":"This work is concerned with the spectral analysis of a piezoelectric energy\u0000harvesting model based on a coupled bending-torsion beam. After building the\u0000problem's operator setting and showing that the governing operator is\u0000nonselfadjoint with a purely discrete spectrum, we derive an asymptotic\u0000approximation of its spectrum. In doing so, we also prove that the addition of\u0000energy harvesting can be viewed as a weak perturbation of the underlying beam\u0000dynamics, in the sense that no piezoelectric parameters appear in the spectral\u0000approximation's first two orders of magnitude. We conclude by outlining future\u0000work based on numerical simulations.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials 具有复径向势的薛定谔算子特征值和的界限
arXiv - MATH - Spectral Theory Pub Date : 2024-08-28 DOI: arxiv-2408.15783
Jean-Claude Cuenin, Solomon Keedle-Isack
{"title":"Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials","authors":"Jean-Claude Cuenin, Solomon Keedle-Isack","doi":"arxiv-2408.15783","DOIUrl":"https://doi.org/arxiv-2408.15783","url":null,"abstract":"We consider eigenvalue sums of Schr\"odinger operators $-Delta+V$ on\u0000$L^2(R^d)$ with complex radial potentials $Vin L^q(R^d)$, $q<d$. We prove\u0000quantitative bounds on the distribution of the eigenvlaues in terms of the\u0000$L^q$ norm of $V$. A consequence of our bounds is that, if the eigenvlaues\u0000$(z_j)$ accumulates to a point in $(0,infty)$, then $(im z_j)$ is summable.\u0000The key technical tools are resolvent estimates in Schatten spaces. We show\u0000that these resolvent estimates follow from spectral measure estimates by an\u0000epsilon removal argument.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hölder continuity of the integrated density of states for Liouville frequencies 刘维尔频率的综合状态密度的荷尔德连续性
arXiv - MATH - Spectral Theory Pub Date : 2024-08-28 DOI: arxiv-2408.15962
Rui Han, Wilhelm Schlag
{"title":"Hölder continuity of the integrated density of states for Liouville frequencies","authors":"Rui Han, Wilhelm Schlag","doi":"arxiv-2408.15962","DOIUrl":"https://doi.org/arxiv-2408.15962","url":null,"abstract":"We prove H\"older continuity of the Lyapunov exponent $L(omega,E)$ and the\u0000integrated density of states at energies that satisfy\u0000$L(omega,E)>4kappa(omega,E)cdot beta(omega)geq 0$ for general analytic\u0000potentials, with $kappa(omega,E)$ being Avila's acceleration.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random eigenvalues of nanotubes 纳米管的随机特征值
arXiv - MATH - Spectral Theory Pub Date : 2024-08-26 DOI: arxiv-2408.14313
Artur Bille, Victor Buchstaber, Pavel Ievlev, Svyatoslav Novikov, Evgeny Spodarev
{"title":"Random eigenvalues of nanotubes","authors":"Artur Bille, Victor Buchstaber, Pavel Ievlev, Svyatoslav Novikov, Evgeny Spodarev","doi":"arxiv-2408.14313","DOIUrl":"https://doi.org/arxiv-2408.14313","url":null,"abstract":"The hexagonal lattice and its dual, the triangular lattice, serve as powerful\u0000models for comprehending the atomic and ring connectivity, respectively, in\u0000textit{graphene} and textit{carbon $(p,q)$--nanotubes}. The chemical and\u0000physical attributes of these two carbon allotropes are closely linked to the\u0000average number of closed paths of different lengths $kinmathbb{N}_0$ on their\u0000respective graph representations. Considering that a carbon $(p,q)$--nanotube\u0000can be thought of as a graphene sheet rolled up in a matter determined by the\u0000textit{chiral vector} $(p,q)$, our findings are based on the study of\u0000textit{random eigenvalues} of both the hexagonal and triangular lattices\u0000presented in cite{bille2023random}. This study reveals that for any given\u0000textit{chiral vector} $(p,q)$, the sequence of counts of closed paths forms a\u0000moment sequence derived from a functional of two independent uniform\u0000distributions. Explicit formulas for key characteristics of these\u0000distributions, including probability density function (PDF) and moment\u0000generating function (MGF), are presented for specific choices of the chiral\u0000vector. Moreover, we demonstrate that as the textit{circumference} of a\u0000$(p,q)$--nanotube approaches infinity, i.e., $p+qrightarrow infty$, the\u0000$(p,q)$--nanotube tends to converge to the hexagonal lattice with respect to\u0000the number of closed paths for any given length $k$, indicating weak\u0000convergence of the underlying distributions.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"153 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142179303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信