Annales Henri Poincaré最新文献

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Classical and Quantised Resolvent Algebras for the Cylinder 圆柱的经典和量化残差代数
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-04-10 DOI: 10.1007/s00023-024-01434-1
T. D. H. van Nuland, R. Stienstra
{"title":"Classical and Quantised Resolvent Algebras for the Cylinder","authors":"T. D. H. van Nuland,&nbsp;R. Stienstra","doi":"10.1007/s00023-024-01434-1","DOIUrl":"10.1007/s00023-024-01434-1","url":null,"abstract":"<div><p>Buchholz and Grundling (Commun Math Phys 272:699–750, 2007) introduced a <span>(hbox {C}^*)</span>-algebra called the resolvent algebra as a canonical quantisation of a symplectic vector space and demonstrated that this algebra has several desirable features. We define an analogue of their resolvent algebra on the cotangent bundle <span>(T^*mathbb {T}^n)</span> of an <i>n</i>-torus by first generalising the classical analogue of the resolvent algebra defined by the first author of this paper in earlier work (van Nuland in J Funct Anal 277:2815–2838, 2019) and subsequently applying Weyl quantisation. We prove that this quantisation is almost strict in the sense of Rieffel and show that our resolvent algebra shares many features with the original resolvent algebra. We demonstrate that both our classical and quantised algebras are closed under the time evolutions corresponding to large classes of potentials. Finally, we discuss their relevance to lattice gauge theory.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 2","pages":"479 - 526"},"PeriodicalIF":1.4,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01434-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567964","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 Number of Eigenvalues of the Dirac Operator in a Bounded Interval 论有界区间内狄拉克算子的特征值个数
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-04-06 DOI: 10.1007/s00023-024-01431-4
Jason Holt, Oleg Safronov
{"title":"On the Number of Eigenvalues of the Dirac Operator in a Bounded Interval","authors":"Jason Holt,&nbsp;Oleg Safronov","doi":"10.1007/s00023-024-01431-4","DOIUrl":"10.1007/s00023-024-01431-4","url":null,"abstract":"<div><p>Let <span>(H_0)</span> be the free Dirac operator and <span>(V geqslant 0)</span> be a positive potential. We study the discrete spectrum of <span>(H(alpha )=H_0-alpha V)</span> in the interval <span>((-1,1))</span> for large values of the coupling constant <span>(alpha &gt;0)</span>. In particular, we obtain an asymptotic formula for the number of eigenvalues of <span>(H(alpha ))</span> situated in a bounded interval <span>([lambda ,mu ))</span> as <span>(alpha rightarrow infty )</span>.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 1","pages":"99 - 121"},"PeriodicalIF":1.4,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01431-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567813","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 Local Central Limit Theorem for Interacting Spin Systems 论相互作用自旋系统的局部中心极限定理
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-04-05 DOI: 10.1007/s00023-024-01433-2
Aldo Procacci, Benedetto Scoppola
{"title":"On the Local Central Limit Theorem for Interacting Spin Systems","authors":"Aldo Procacci,&nbsp;Benedetto Scoppola","doi":"10.1007/s00023-024-01433-2","DOIUrl":"10.1007/s00023-024-01433-2","url":null,"abstract":"<div><p>We prove the equivalence between integral and local central limit theorem for spin system interacting via an absolutely summable pair potential without any conditions on the temperature of the system.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5349 - 5366"},"PeriodicalIF":1.4,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140567899","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
Instability of Electroweak Homogeneous Vacua in Strong Magnetic Fields 强磁场中的电弱同质虚空的不稳定性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-19 DOI: 10.1007/s00023-024-01430-5
Adam Gardner, Israel Michael Sigal
{"title":"Instability of Electroweak Homogeneous Vacua in Strong Magnetic Fields","authors":"Adam Gardner,&nbsp;Israel Michael Sigal","doi":"10.1007/s00023-024-01430-5","DOIUrl":"10.1007/s00023-024-01430-5","url":null,"abstract":"<div><p>We consider the classical vacua of the Weinberg–Salam (WS) model of electroweak forces. These are no-particle, static solutions to the WS equations minimizing the WS energy locally. We study the WS vacuum solutions exhibiting a non-vanishing average magnetic field of strength <i>b</i> and prove that (i) there is a magnetic field threshold <span>(b_*)</span> such that for <span>(b&lt;b_*)</span>, the vacua are translationally invariant (and the magnetic field is constant), while, for <span>(b&gt;b_*)</span>, they are not, (ii) for <span>(b&gt;b_*)</span>, there are non-translationally invariant solutions with lower energy per unit volume and with the discrete translational symmetry of a 2D lattice in the plane transversal to <i>b</i>, and (iii) the lattice minimizing the energy per unit volume approaches the hexagonal one as the magnetic field strength approaches the threshold <span>(b_*)</span>. In the absence of particles, the Weinberg–Salam model reduces to the Yang–Mills–Higgs (YMH) equations for the gauge group <i>U</i>(2). Thus, our results can be rephrased as the corresponding statements about the <i>U</i>(2)-YMH equations.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5277 - 5337"},"PeriodicalIF":1.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01430-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197410","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
Null Hamiltonian Yang–Mills theory: Soft Symmetries and Memory as Superselection 空哈密顿杨-米尔斯理论:软对称和超选择记忆
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-19 DOI: 10.1007/s00023-024-01428-z
A. Riello, M. Schiavina
{"title":"Null Hamiltonian Yang–Mills theory: Soft Symmetries and Memory as Superselection","authors":"A. Riello,&nbsp;M. Schiavina","doi":"10.1007/s00023-024-01428-z","DOIUrl":"10.1007/s00023-024-01428-z","url":null,"abstract":"<div><p>Soft symmetries for Yang–Mills theory are shown to correspond to the residual Hamiltonian action of the gauge group on the Ashtekar–Streubel phase space, which is the result of a partial symplectic reduction. The associated momentum map is the electromagnetic memory in the Abelian theory, or a nonlinear, gauge-equivariant, generalisation thereof in the non-Abelian case. This result follows from an application of Hamiltonian reduction by stages, enabled by the existence of a natural normal subgroup of the gauge group on a null codimension-1 submanifold with boundaries. The first stage is coisotropic reduction of the Gauss constraint, and it yields a symplectic extension of the Ashtekar–Streubel phase space (up to a covering). Hamiltonian reduction of the residual gauge action leads to the fully reduced phase space of the theory. This is a Poisson manifold, whose symplectic leaves, called superselection sectors, are labelled by the (gauge classes of the generalised) electric flux across the boundary. In this framework, the Ashtekar–Streubel phase space arises as an intermediate reduction stage that enforces the superselection of the electric flux at only one of the two boundary components. These results provide a natural, purely Hamiltonian, explanation of the existence of soft symmetries as a byproduct of partial symplectic reduction, as well as a motivation for the expected decomposition of the quantum Hilbert space of states into irreducible representations labelled by the Casimirs of the Poisson structure on the reduced phase space.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 2","pages":"389 - 477"},"PeriodicalIF":1.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01428-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197399","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
Structural Stability of the RG Flow in the Gross–Neveu Model 格罗斯-涅乌模型中 RG 流的结构稳定性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-18 DOI: 10.1007/s00023-024-01427-0
J. Dimock, Cheng Yuan
{"title":"Structural Stability of the RG Flow in the Gross–Neveu Model","authors":"J. Dimock,&nbsp;Cheng Yuan","doi":"10.1007/s00023-024-01427-0","DOIUrl":"10.1007/s00023-024-01427-0","url":null,"abstract":"<div><p>We study flow of renormalization group (RG) transformations for the massless Gross–Neveu model in a non-perturbative formulation. The model is defined on a two-dimensional Euclidean space with a finite volume. The quadratic approximation to the flow stays bounded after suitable renormalization. We show that for weak coupling this property also is true for the complete flow. As an application we prove an ultraviolet stability bound for the model. Our treatment is an application of a method of Bauerschmidt, Brydges, and Slade. The method was developed for an infrared problem and is now applied to an ultraviolet problem.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5113 - 5186"},"PeriodicalIF":1.4,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152346","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
An Index for Quantum Cellular Automata on Fusion Spin Chains 融合自旋链上的量子蜂窝自动机索引
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-11 DOI: 10.1007/s00023-024-01429-y
Corey Jones, Junhwi Lim
{"title":"An Index for Quantum Cellular Automata on Fusion Spin Chains","authors":"Corey Jones,&nbsp;Junhwi Lim","doi":"10.1007/s00023-024-01429-y","DOIUrl":"10.1007/s00023-024-01429-y","url":null,"abstract":"<div><p>Interpreting the GNVW index for 1D quantum cellular automata (QCA) in terms of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators of 2D topological codes. We show that for the fusion spin chains built from the fusion category <span>(textbf{Fib})</span>, the index is a complete invariant for the group of QCA modulo finite depth circuits.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 10","pages":"4399 - 4422"},"PeriodicalIF":1.4,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140097785","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
Synchronous Values of Games 游戏的同步价值
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-04 DOI: 10.1007/s00023-024-01426-1
J. William Helton, Hamoon Mousavi, Seyed Sajjad Nezhadi, Vern I. Paulsen, Travis B. Russell
{"title":"Synchronous Values of Games","authors":"J. William Helton,&nbsp;Hamoon Mousavi,&nbsp;Seyed Sajjad Nezhadi,&nbsp;Vern I. Paulsen,&nbsp;Travis B. Russell","doi":"10.1007/s00023-024-01426-1","DOIUrl":"10.1007/s00023-024-01426-1","url":null,"abstract":"<div><p>We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give examples of synchronous games, in particular graph colouring games, with synchronous value that is strictly smaller than their ordinary value. Thus, the optimal strategy for a synchronous game need not be synchronous. We derive a formula for the synchronous value of an XOR game as an optimization problem over a spectrahedron involving a matrix related to the cost matrix. We give an example of a game such that the synchronous value of repeated products of the game is strictly increasing. We show that the synchronous quantum bias of the XOR of two XOR games is not multiplicative. Finally, we derive geometric and algebraic conditions that a set of projections that yields the synchronous value of a game must satisfy.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 10","pages":"4357 - 4397"},"PeriodicalIF":1.4,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034231","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
Nodal Set Openings on Perturbed Rectangular Domains 扰动矩形域上的节点集开口
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-02 DOI: 10.1007/s00023-024-01424-3
Thomas Beck, Marichi Gupta, Jeremy Marzuola
{"title":"Nodal Set Openings on Perturbed Rectangular Domains","authors":"Thomas Beck,&nbsp;Marichi Gupta,&nbsp;Jeremy Marzuola","doi":"10.1007/s00023-024-01424-3","DOIUrl":"10.1007/s00023-024-01424-3","url":null,"abstract":"<div><p>We study the effects of perturbing the boundary of a rectangle on the nodal sets of eigenfunctions of the Laplacian. Namely, for a rectangle of a given aspect ratio <i>N</i>, we identify the first Dirichlet mode to feature a crossing in its nodal set and perturb one of the sides of the rectangle by a close to flat, smooth curve. Such perturbations will often “open” the crossing in the nodal set, splitting it into two curves, and we study the separation between these curves and their regularity. The main technique used is an approximate separation of variables that allows us to restrict study to the first two Fourier modes in an eigenfunction expansion. We show how the nature of the boundary perturbation provides conditions on the orientation of the opening and estimates on its size. In particular, several features of the perturbed nodal set are asymptotically independent of the aspect ratio, which contrasts with prior works. Numerical results supporting our findings are also presented.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 11","pages":"4889 - 4929"},"PeriodicalIF":1.4,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019049","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
On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang–Mills Equation 论还原准经典自偶杨-米尔斯方程的完全非局部对称递归算子
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-03-01 DOI: 10.1007/s00023-024-01425-2
Jiřina Jahnová, Petr Vojčák
{"title":"On Recursion Operators for Full-Fledged Nonlocal Symmetries of the Reduced Quasi-classical Self-dual Yang–Mills Equation","authors":"Jiřina Jahnová,&nbsp;Petr Vojčák","doi":"10.1007/s00023-024-01425-2","DOIUrl":"10.1007/s00023-024-01425-2","url":null,"abstract":"<div><p>We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang–Mills equation. It turns out that the discovered recursion operators can be interpreted as infinite-dimensional matrices of differential functions which act on the generating vector functions of the nonlocal symmetries simply by matrix multiplication. To the best of our knowledge, there are no other examples of such recursion operators in the literature so far, so our approach is completely innovative. Further, we investigate the algebraic properties of the discovered operators and discuss the <span>({mathbb {R}})</span>-algebra structure on the set of all recursion operators for full-fledged nonlocal symmetries of the equation in question. Finally, we illustrate the action of the obtained recursion operators on particularly chosen full-fledged symmetries and emphasize their advantages compared to the action of traditionally used recursion operators for shadows.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 10","pages":"4633 - 4669"},"PeriodicalIF":1.4,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01425-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019045","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
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