arXiv - MATH - Spectral Theory最新文献_第7页

Adelic and Rational Grassmannians for finite dimensional algebras 有限维代数的阿德利和有理格拉斯曼

arXiv - MATH - Spectral Theory Pub Date : 2024-08-08 DOI: arxiv-2408.04355

Emil Horozov, Milen Yakimov

引用次数: 0

Geometric bounds for low Steklov eigenvalues of finite volume hyperbolic surfaces 有限体积双曲面低斯特克洛夫特征值的几何边界

arXiv - MATH - Spectral Theory Pub Date : 2024-08-08 DOI: arxiv-2408.04534

Asma Hassannezhad, Antoine Métras, Hélène Perrin

引用次数: 0

Wave packet decomposition for Schrodinger evolution with rough potential and generic value of parameter 具有粗糙势和一般参数值的薛定谔演化的波包分解

arXiv - MATH - Spectral Theory Pub Date : 2024-08-06 DOI: arxiv-2408.03470

Sergey A. Denisov

引用次数: 0

From resolvent expansions at zero to long time wave expansions 从零点分解展开到长时波展开

arXiv - MATH - Spectral Theory Pub Date : 2024-08-06 DOI: arxiv-2408.03234

T. J. Christiansen, K. Datchev, M. Yang

引用次数: 0

Low energy resolvent asymptotics of the multipole Aharonov--Bohm Hamiltonian 多极阿哈诺夫--玻姆哈密顿的低能解析渐近论

arXiv - MATH - Spectral Theory Pub Date : 2024-08-06 DOI: arxiv-2408.03233

T. J. Christiansen, K. Datchev, M. Yang

引用次数: 0

Scattering theory for $C^2$ long-range potentials C^2$长程电位的散射理论

arXiv - MATH - Spectral Theory Pub Date : 2024-08-06 DOI: arxiv-2408.02979

K. Ito, E. Skibsted

{"title":"Scattering theory for $C^2$ long-range potentials","authors":"K. Ito, E. Skibsted","doi":"arxiv-2408.02979","DOIUrl":"https://doi.org/arxiv-2408.02979","url":null,"abstract":"We develop a complete stationary scattering theory for Schr\"odinger\u0000operators on $mathbb R^d$, $dge 2$, with $C^2$ long-range potentials. This\u0000extends former results in the literature, in particular [Is1, Is2, II, GY],\u0000which all require a higher degree of smoothness. In this sense the spirit of\u0000our paper is similar to [H\"o2, Chapter XXX], which also develops a scattering\u0000theory under the $C^2$ condition, however being very different from ours. While\u0000the Agmon-H\"ormander theory is based on the Fourier transform, our theory is\u0000not and may be seen as more related to our previous approach to scattering\u0000theory on manifolds [IS1,IS2,IS3]. The $C^2$ regularity is natural in the\u0000Agmon-H\"ormander theory as well as in our theory, in fact probably being\u0000`optimal' in the Euclidean setting. We prove equivalence of the stationary and\u0000time-dependent theories by giving stationary representations of associated\u0000time-dependent wave operators. Furthermore we develop a related stationary\u0000scattering theory at fixed energy in terms of asymptotics of generalized\u0000eigenfunctions of minimal growth. A basic ingredient of our approach is a\u0000solution to the eikonal equation constructed from the geometric variational\u0000scheme of [CS]. Another key ingredient is strong radiation condition bounds for\u0000the limiting resolvents originating in [HS]. They improve formerly known ones\u0000[Is1, Sa] and considerably simplify the stationary approach. We obtain the\u0000bounds by a new commutator scheme whose elementary form allows a small degree\u0000of smoothness.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943890","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 statistics of the Laplacian on random covers of a closed negatively curved surface 封闭负弯曲表面随机盖上的拉普拉斯函数谱统计

arXiv - MATH - Spectral Theory Pub Date : 2024-08-05 DOI: arxiv-2408.02808

Julien Moy

{"title":"Spectral statistics of the Laplacian on random covers of a closed negatively curved surface","authors":"Julien Moy","doi":"arxiv-2408.02808","DOIUrl":"https://doi.org/arxiv-2408.02808","url":null,"abstract":"Let $(X,g)$ be a closed, connected surface, with variable negative curvature.\u0000We consider the distribution of eigenvalues of the Laplacian on random covers\u0000$X_nto X$ of degree $n$. We focus on the ensemble variance of the smoothed\u0000number of eigenvalues of the square root of the positive Laplacian\u0000$sqrt{Delta}$ in windows $[lambda-frac 1L,lambda+frac 1L]$, over the set\u0000of $n$-sheeted covers of $X$. We first take the limit of large degree $nto\u0000+infty$, then we let the energy $lambda$ go to $+infty$ while the window\u0000size $frac 1L$ goes to $0$. In this ad hoc limit, local energy averages of the\u0000variance converge to an expression corresponding to the variance of the same\u0000statistic when considering instead spectra of large random matrices of the\u0000Gaussian Orthogonal Ensemble (GOE). By twisting the Laplacian with unitary\u0000representations, we are able to observe different statistics, corresponding to\u0000the Gaussian Unitary Ensemble (GUE) when time reversal symmetry is broken.\u0000These results were shown by F. Naud for the model of random covers of a\u0000hyperbolic surface. For an individual cover $X_nto X$, we consider spectral fluctuations of the\u0000counting function on $X_n$ around the ensemble average. In the large energy\u0000regime, for a typical cover $X_nto X$ of large degree, these fluctuations are\u0000shown to approach the GOE result, a phenomenon called ergodicity in Random\u0000Matrix Theory. An analogous result for random covers of hyperbolic surfaces was\u0000obtained by Y. Maoz.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943886","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

Green's function estimates for quasi-periodic operators on $mathbb{Z}^d$ with power-law long-range hopping 具有幂律长程跳变的 $mathbb{Z}^d$ 上准周期算子的格林函数估计值

arXiv - MATH - Spectral Theory Pub Date : 2024-08-04 DOI: arxiv-2408.01913

Yunfeng Shi, Li Wen

引用次数: 0

On Landis conjecture for positive Schrödinger operators on graphs 关于图上正薛定谔算子的兰迪斯猜想

arXiv - MATH - Spectral Theory Pub Date : 2024-08-04 DOI: arxiv-2408.02149

Ujjal Das, Matthias Keller, Yehuda Pinchover

引用次数: 0

Restriction of Schrödinger eigenfunctions to submanifolds 薛定谔特征函数对子曲面的限制

arXiv - MATH - Spectral Theory Pub Date : 2024-08-04 DOI: arxiv-2408.01947

Xiaoqi Huang, Xing Wang, Cheng Zhang

引用次数: 0