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Annales Henri Poincaré最新文献

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Differences Between Robin and Neumann Eigenvalues on Metric Graphs 度量图上罗宾特征值与诺依曼特征值的区别
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-19 DOI: 10.1007/s00023-023-01401-2
Ram Band, Holger Schanz, Gilad Sofer
{"title":"Differences Between Robin and Neumann Eigenvalues on Metric Graphs","authors":"Ram Band,&nbsp;Holger Schanz,&nbsp;Gilad Sofer","doi":"10.1007/s00023-023-01401-2","DOIUrl":"10.1007/s00023-023-01401-2","url":null,"abstract":"<div><p>We consider the Laplacian on a metric graph, equipped with Robin (<span>(delta )</span>-type) vertex condition at some of the graph vertices and Neumann–Kirchhoff condition at all others. The corresponding eigenvalues are called Robin eigenvalues, whereas they are called Neumann eigenvalues if the Neumann–Kirchhoff condition is imposed at all vertices. The sequence of differences between these pairs of eigenvalues is called the Robin–Neumann gap. We prove that the limiting mean value of this sequence exists and equals a geometric quantity, analogous to the one obtained for planar domains by Rudnick et al. (Commun Math Phys, 2021. arXiv:2008.07400). Moreover, we show that the sequence is uniformly bounded and provide explicit upper and lower bounds. We also study the possible accumulation points of the sequence and relate those to the associated probability distribution of the gaps. To prove our main results, we prove a local Weyl law, as well as explicit expressions for the second moments of the eigenfunction scattering amplitudes.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3859 - 3898"},"PeriodicalIF":1.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138817349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions 具有缺陷指数 (k, k) 的算子及其自相关扩展的收敛性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-12 DOI: 10.1007/s00023-023-01397-9
August Bjerg
{"title":"Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions","authors":"August Bjerg","doi":"10.1007/s00023-023-01397-9","DOIUrl":"10.1007/s00023-023-01397-9","url":null,"abstract":"<div><p>We consider an abstract sequence <span>({A_n}_{n=1}^infty )</span> of closed symmetric operators on a separable Hilbert space <span>({mathcal {H}})</span>. It is assumed that all <span>(A_n)</span>’s have equal deficiency indices (<i>k</i>, <i>k</i>) and thus self-adjoint extensions <span>({B_n}_{n=1}^infty )</span> exist and are parametrized by partial isometries <span>({U_n}_{n=1}^infty )</span> on <span>({mathcal {H}})</span> according to von Neumann’s extension theory. Under two different convergence assumptions on the <span>(A_n)</span>’s we give the precise connection between strong resolvent convergence of the <span>(B_n)</span>’s and strong convergence of the <span>(U_n)</span>’s.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 6","pages":"2995 - 3007"},"PeriodicalIF":1.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01397-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139370810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Recurrence Relations and General Solution of the Exceptional Hermite Equation 递推关系和赫米特方程的一般解法
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-12 DOI: 10.1007/s00023-023-01395-x
Alfred Michel Grundland, Danilo Latini, Ian Marquette
{"title":"Recurrence Relations and General Solution of the Exceptional Hermite Equation","authors":"Alfred Michel Grundland,&nbsp;Danilo Latini,&nbsp;Ian Marquette","doi":"10.1007/s00023-023-01395-x","DOIUrl":"10.1007/s00023-023-01395-x","url":null,"abstract":"<div><p>Exceptional orthogonal Hermite polynomials have been linked to the k-step extension of the harmonic oscillator. The exceptional polynomials allow the existence of different supercharges in the Darboux–Crum and Krein–Adler constructions. They also allow the existence of different types of ladder relations and their associated recurrence relations. The existence of such relations is a unique property of these polynomials. Those relations have been used to construct 2D models which are superintegrable and display an interesting spectrum, degeneracies and finite-dimensional unitary representations. In previous works, only the physical or polynomial part of the spectrum was discussed. It is known that the general solutions are associated with other types of recurrence/ladder relations. We discuss in detail the case of the exceptional Hermite polynomials <span>(X_2^{(1)})</span> and explicitly present new chains obtained by acting with different types of ladder operators. We exploit a recent result by one of the authors (Chalifour and Grundland in Ann Henri Poincaré 21:3341, 2020), where the general analytic solution was constructed and connected with the non-degenerate confluent Heun equation. The analogue Rodrigues formulas for the general solution are constructed. The set of finite states from which the other states can be obtained algebraically is not unique, but the vanishing arrow and diagonal arrow from the diagram of the 2-chain representations can be used to obtain minimal sets. These Rodrigues formulas are then exploited, not only to construct the states, polynomial and non-polynomial, in a purely algebraic way, but also to obtain coefficients from the action of ladder operators in an algebraic manner based on further commutation relations between monomials in the generators.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3779 - 3804"},"PeriodicalIF":1.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unitary, Anomalous Master Ward Identity and its Connections to the Wess–Zumino Condition, BV Formalism and (L_infty )-algebras 单元反常主沃德同一性及其与韦斯-祖米诺条件、BV 形式主义和 $$L_infty $$ - 算法的联系
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-12 DOI: 10.1007/s00023-023-01388-w
Romeo Brunetti, Michael Dütsch, Klaus Fredenhagen, Kasia Rejzner
{"title":"Unitary, Anomalous Master Ward Identity and its Connections to the Wess–Zumino Condition, BV Formalism and (L_infty )-algebras","authors":"Romeo Brunetti,&nbsp;Michael Dütsch,&nbsp;Klaus Fredenhagen,&nbsp;Kasia Rejzner","doi":"10.1007/s00023-023-01388-w","DOIUrl":"10.1007/s00023-023-01388-w","url":null,"abstract":"<div><p>The C*-algebraic construction of QFT by Buchholz and one of us relies on the causal structure of space-time and a classical Lagrangian. In one of our previous papers, we have introduced additional structure into this construction, namely an action of symmetries, which is related to fixing renormalization conditions. This action characterizes anomalies and satisfies a cocycle condition which is summarized in the unitary anomalous Master Ward identity. Here (using perturbation theory) we show how this cocycle condition is related to the Wess–Zumino consistency relation and the consistency relation for the anomaly in the BV formalism, where the latter follows from the generalized Jacobi identity for the associated <span>(L_infty )</span>-algebra. In addition, we give a proof that perturbative agreement (i.e., independence of a perturbative QFT on the splitting of the Lagrangian into free and interacting parts) can be achieved by finite renormalizations.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 5","pages":"2547 - 2583"},"PeriodicalIF":1.4,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01388-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Fourier Analysis of the Einstein–Klein–Gordon System: Growth and Decay of the Fourier Constants 关于爱因斯坦-克莱因-戈登系统的傅立叶分析：傅立叶常数的增长与衰减
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-09 DOI: 10.1007/s00023-023-01393-z
Athanasios Chatzikaleas
{"title":"On the Fourier Analysis of the Einstein–Klein–Gordon System: Growth and Decay of the Fourier Constants","authors":"Athanasios Chatzikaleas","doi":"10.1007/s00023-023-01393-z","DOIUrl":"10.1007/s00023-023-01393-z","url":null,"abstract":"<div><p>We consider the <span>((1+3))</span>-dimensional Einstein equations with negative cosmological constant coupled to a spherically symmetric, massless scalar field and study perturbations around the anti-de Sitter spacetime. We derive the resonant systems, pick out vanishing secular terms and discuss issues related to small divisors. Most importantly, we rigorously establish (sharp, in most of the cases) asymptotic behaviour for all the interaction coefficients. The latter is based on uniform estimates for the eigenfunctions associated to the linearized operator as well as on some oscillatory integrals.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 6","pages":"3009 - 3079"},"PeriodicalIF":1.4,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01393-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138561543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Expansion and Collapse of Spherically Symmetric Isotropic Elastic Bodies Surrounded by Vacuum 被真空包围的球面对称各向同性弹性体的膨胀和坍缩
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-09 DOI: 10.1007/s00023-023-01390-2
Thomas C. Sideris
{"title":"Expansion and Collapse of Spherically Symmetric Isotropic Elastic Bodies Surrounded by Vacuum","authors":"Thomas C. Sideris","doi":"10.1007/s00023-023-01390-2","DOIUrl":"10.1007/s00023-023-01390-2","url":null,"abstract":"<div><p>A class of isotropic and scale-invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time, depending on the sign of the residual pressure. The bodies are surrounded by vacuum so that the boundary surface forces vanish, while the density remains strictly positive. The body is subject only to internal elastic stress.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 7","pages":"3529 - 3562"},"PeriodicalIF":1.4,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01390-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138561697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Characteristic Gluing Problem for the Einstein Vacuum Equations: Linear and Nonlinear Analysis 爱因斯坦真空方程的特性胶合问题：线性与非线性分析
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-07 DOI: 10.1007/s00023-023-01394-y
Stefanos Aretakis, Stefan Czimek, Igor Rodnianski
{"title":"The Characteristic Gluing Problem for the Einstein Vacuum Equations: Linear and Nonlinear Analysis","authors":"Stefanos Aretakis,&nbsp;Stefan Czimek,&nbsp;Igor Rodnianski","doi":"10.1007/s00023-023-01394-y","DOIUrl":"10.1007/s00023-023-01394-y","url":null,"abstract":"<div><p>This is the second paper in a series of papers addressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-10 characteristic gluing problem for characteristic data which are close to the Minkowski data. We derive an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges that are conserved by the linearized null constraint equations and act as obstructions to the gluing problem. The gauge-dependent charges can be matched by applying angular and transversal gauge transformations of the characteristic data. By making use of a special hierarchy of radial weights of the null constraint equations, we construct the null lapse function and the conformal geometry of the characteristic hypersurface, and we show that the aforementioned charges are in fact the only obstructions to the gluing problem. Modulo the gauge-invariant charges, the resulting solution of the null constraint equations is <span>(C^{m+2})</span> for any specified integer <span>(mge 0)</span> in the tangential directions and <span>(C^2)</span> in the transversal directions to the characteristic hypersurface. We also show that higher-order (in all directions) gluing is possible along bifurcated characteristic hypersurfaces (modulo the gauge-invariant charges).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 6","pages":"3081 - 3205"},"PeriodicalIF":1.4,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138554434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Particle Trajectories for Quantum Maps 量子映射的粒子轨迹
IF 1.5 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-11-27 DOI: 10.1007/s00023-023-01387-x
Yonah Borns-Weil, Izak Oltman
{"title":"Particle Trajectories for Quantum Maps","authors":"Yonah Borns-Weil, Izak Oltman","doi":"10.1007/s00023-023-01387-x","DOIUrl":"https://doi.org/10.1007/s00023-023-01387-x","url":null,"abstract":"<p>We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by the propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is “less chaotic.” In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"117 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539446","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Particle Trajectories for Quantum Maps 量子映射的粒子轨迹
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-11-27 DOI: 10.1007/s00023-023-01387-x
Yonah Borns-Weil, Izak Oltman
{"title":"Particle Trajectories for Quantum Maps","authors":"Yonah Borns-Weil,&nbsp;Izak Oltman","doi":"10.1007/s00023-023-01387-x","DOIUrl":"10.1007/s00023-023-01387-x","url":null,"abstract":"<div><p>We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by the propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is “less chaotic.” In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3699 - 3738"},"PeriodicalIF":1.4,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01387-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-trivial Bundles and Algebraic Classical Field Theory 非平凡束与代数经典场论
IF 1.5 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-11-22 DOI: 10.1007/s00023-023-01386-y
Romeo Brunetti, Andrea Moro
{"title":"Non-trivial Bundles and Algebraic Classical Field Theory","authors":"Romeo Brunetti, Andrea Moro","doi":"10.1007/s00023-023-01386-y","DOIUrl":"https://doi.org/10.1007/s00023-023-01386-y","url":null,"abstract":"<p>Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e., appropriate smooth functions on them. The kinematics will be further specified by means of the Peierls brackets, which in turn are defined via the causal propagators of linearized field equations. We shall compare the formalism we use with the more traditional ones.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"191 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138539487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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