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Annales Henri Poincaré最新文献

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Shuffling Algorithm for Coupled Tilings of the Aztec Diamond 阿兹台克钻石耦合平顶的洗牌算法
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-27 DOI: 10.1007/s00023-023-01407-w
David Keating, Matthew Nicoletti
{"title":"Shuffling Algorithm for Coupled Tilings of the Aztec Diamond","authors":"David Keating,&nbsp;Matthew Nicoletti","doi":"10.1007/s00023-023-01407-w","DOIUrl":"10.1007/s00023-023-01407-w","url":null,"abstract":"<div><p>In this article, we define a generalization of the domino shuffling algorithm for tilings of the Aztec diamond to the interacting <i>k</i>-tilings recently introduced by S. Corteel, A. Gitlin, and the first author. We describe the algorithm both in terms of dynamics on a system of colored particles and as operations on the dominos themselves.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 12","pages":"5187 - 5229"},"PeriodicalIF":1.4,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01407-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139579088","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
Baxter Operators in Ruijsenaars Hyperbolic System III: Orthogonality and Completeness of Wave Functions Ruijsenaars 双曲系统中的巴克斯特算子 III：波函数的正交性和完备性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-22 DOI: 10.1007/s00023-023-01406-x
N. Belousov, S. Derkachov, S. Kharchev, S. Khoroshkin
{"title":"Baxter Operators in Ruijsenaars Hyperbolic System III: Orthogonality and Completeness of Wave Functions","authors":"N. Belousov,&nbsp;S. Derkachov,&nbsp;S. Kharchev,&nbsp;S. Khoroshkin","doi":"10.1007/s00023-023-01406-x","DOIUrl":"10.1007/s00023-023-01406-x","url":null,"abstract":"<div><p>In the previous paper, we showed that the wave functions of the quantum Ruijsenaars hyperbolic system diagonalize Baxter <i>Q</i>-operators. Using this property and duality relation, we prove orthogonality and completeness relations for the wave functions or, equivalently, unitarity of the corresponding integral transform.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 7","pages":"3297 - 3332"},"PeriodicalIF":1.4,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139553632","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 the Convergence to the Non-equilibrium Steady State of a Langevin Dynamics with Widely Separated Time Scales and Different Temperatures 论时间尺度相距甚远且温度不同的朗格文动力学非平衡稳态的收敛性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-18 DOI: 10.1007/s00023-023-01392-0
Diego Alberici, Nicolas Macris, Emanuele Mingione
{"title":"On the Convergence to the Non-equilibrium Steady State of a Langevin Dynamics with Widely Separated Time Scales and Different Temperatures","authors":"Diego Alberici,&nbsp;Nicolas Macris,&nbsp;Emanuele Mingione","doi":"10.1007/s00023-023-01392-0","DOIUrl":"10.1007/s00023-023-01392-0","url":null,"abstract":"<div><p>We study the solution of the two-temperature Fokker–Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of convergence are estimated assuming the validity of logarithmic Sobolev inequalities for the conditional and marginal distributions of the limit measure. We show that these estimates are sharp in the exactly solvable case of a quadratic potential. We discuss a few examples where the logarithmic Sobolev inequalities are satisfied through simple, though not optimal, criteria. In particular, we consider a spin glass model with slowly varying external magnetic fields whose non-equilibrium measure corresponds to Guerra’s hierarchical construction appearing in Talagrand’s proof of the Parisi formula.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 7","pages":"3405 - 3466"},"PeriodicalIF":1.4,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496616","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
Frobenius Algebras Associated with the (alpha )-Induction for Equivariantly Braided Tensor Categories 与等辫张量范畴的 $$alpha $$ -Induction 相关的弗罗贝尼斯代数
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-16 DOI: 10.1007/s00023-023-01396-w
Mizuki Oikawa
{"title":"Frobenius Algebras Associated with the (alpha )-Induction for Equivariantly Braided Tensor Categories","authors":"Mizuki Oikawa","doi":"10.1007/s00023-023-01396-w","DOIUrl":"10.1007/s00023-023-01396-w","url":null,"abstract":"<div><p>Let <i>G</i> be a group. We give a categorical definition of the <i>G</i>-equivariant <span>(alpha )</span>-induction associated with a given <i>G</i>-equivariant Frobenius algebra in a <i>G</i>-braided multitensor category, which generalizes the <span>(alpha )</span>-induction for <i>G</i>-twisted representations of conformal nets. For a given <i>G</i>-equivariant Frobenius algebra in a spherical <i>G</i>-braided fusion category, we construct a <i>G</i>-equivariant Frobenius algebra, which we call a <i>G</i>-equivariant <span>(alpha )</span>-induction Frobenius algebra, in a suitably defined category called neutral double. This construction generalizes Rehren’s construction of <span>(alpha )</span>-induction Q-systems. Finally, we define the notion of the <i>G</i>-equivariant full centre of a <i>G</i>-equivariant Frobenius algebra in a spherical <i>G</i>-braided fusion category and show that it indeed coincides with the corresponding <i>G</i>-equivariant <span>(alpha )</span>-induction Frobenius algebra, which generalizes a theorem of Bischoff, Kawahigashi and Longo.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 10","pages":"4423 - 4495"},"PeriodicalIF":1.4,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01396-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482330","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
Global Existence and Long-Time Behavior in the 1 + 1-Dimensional Principal Chiral Model with Applications to Solitons 1 + 1 维主手性模型中的全局存在性和长时间行为及其对孤子的应用
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-16 DOI: 10.1007/s00023-023-01405-y
Jessica Trespalacios
{"title":"Global Existence and Long-Time Behavior in the 1 + 1-Dimensional Principal Chiral Model with Applications to Solitons","authors":"Jessica Trespalacios","doi":"10.1007/s00023-023-01405-y","DOIUrl":"10.1007/s00023-023-01405-y","url":null,"abstract":"<div><p>In this paper, we consider the 1 + 1-dimensional vector-valued principal chiral field model (PCF) obtained as a simplification of the vacuum Einstein field equations under the Belinski–Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally, some applications are presented in the case of PCF solitons, a first step toward the study of its nonlinear stability.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 11","pages":"4671 - 4712"},"PeriodicalIF":1.4,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482084","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
Circuit Equation of Grover Walk 格罗弗漫步线路方程
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-10 DOI: 10.1007/s00023-023-01389-9
Yusuke Higuchi, Etsuo Segawa
{"title":"Circuit Equation of Grover Walk","authors":"Yusuke Higuchi,&nbsp;Etsuo Segawa","doi":"10.1007/s00023-023-01389-9","DOIUrl":"10.1007/s00023-023-01389-9","url":null,"abstract":"<div><p>We consider the Grover walk on the infinite graph in which an internal finite subgraph receives the inflow from the outside with some frequency and also radiates the outflow to the outside. To characterize the stationary state of this system, which is represented by a function on the arcs of the graph, we introduce a kind of discrete gradient operator twisted by the frequency. Then, we obtain a circuit equation which shows that (i) the stationary state is described by the twisted gradient of a potential function which is a function on the vertices; (ii) the potential function satisfies the Poisson equation with respect to a generalized Laplacian matrix. Consequently, we characterize the scattering on the surface of the internal graph and the energy penetrating inside it. Moreover, for the complete graph as the internal graph, we illustrate the relationship of the scattering and the internal energy to the frequency and the number of tails.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3739 - 3777"},"PeriodicalIF":1.4,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421920","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
The Singularities of Selberg- and Dotsenko–Fateev-Like Integrals 塞尔伯格积分和多森科-法捷耶夫积分的奇异性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-01-03 DOI: 10.1007/s00023-023-01402-1
Ethan Sussman
{"title":"The Singularities of Selberg- and Dotsenko–Fateev-Like Integrals","authors":"Ethan Sussman","doi":"10.1007/s00023-023-01402-1","DOIUrl":"10.1007/s00023-023-01402-1","url":null,"abstract":"<div><p>We discuss the meromorphic continuation of certain hypergeometric integrals modeled on the Selberg integral, including the 3-point and 4-point functions of BPZ’s minimal models of 2D CFT as described by Felder &amp; Silvotti and Dotsenko &amp; Fateev (the “Coulomb gas formalism”). This is accomplished via a geometric analysis of the singularities of the integrands. In the case that the integrand is symmetric (as in the Selberg integral itself) or, more generally, what we call “DF-symmetric,” we show that a number of apparent singularities are removable, as required for the construction of the minimal models via these methods.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 9","pages":"3957 - 4032"},"PeriodicalIF":1.4,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01402-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095853","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
Robustness of Flat Bands on the Perturbed Kagome and the Perturbed Super-Kagome Lattice 扰动卡戈米晶格和扰动超卡戈米晶格上平带的稳健性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-28 DOI: 10.1007/s00023-023-01399-7
Joachim Kerner, Matthias Täufer, Jens Wintermayr
{"title":"Robustness of Flat Bands on the Perturbed Kagome and the Perturbed Super-Kagome Lattice","authors":"Joachim Kerner,&nbsp;Matthias Täufer,&nbsp;Jens Wintermayr","doi":"10.1007/s00023-023-01399-7","DOIUrl":"10.1007/s00023-023-01399-7","url":null,"abstract":"<div><p>We study spectral properties of perturbed discrete Laplacians on two-dimensional Archimedean tilings. The perturbation manifests itself in the introduction of non-trivial edge weights. We focus on the two lattices on which the unperturbed Laplacian exhibits flat bands, namely the <span>((3.6)^2)</span> Kagome lattice and the <span>((3.12^2))</span> “Super-Kagome” lattice. We characterize all possible choices for edge weights which lead to flat bands. Furthermore, we discuss spectral consequences such as the emergence of new band gaps. Among our main findings is that flat bands are robust under physically reasonable assumptions on the perturbation, and we completely describe the perturbation-spectrum phase diagram. The two flat bands in the Super-Kagome lattice are shown to even exhibit an “all-or-nothing” phenomenon in the sense that there is no perturbation, which can destroy only one flat band while preserving the other.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3831 - 3857"},"PeriodicalIF":1.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01399-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066227","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
Stability of the Spectral Gap and Ground State Indistinguishability for a Decorated AKLT Model 装饰 AKLT 模型的光谱间隙稳定性和基态可分辨性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-27 DOI: 10.1007/s00023-023-01398-8
Angelo Lucia, Alvin Moon, Amanda Young
{"title":"Stability of the Spectral Gap and Ground State Indistinguishability for a Decorated AKLT Model","authors":"Angelo Lucia,&nbsp;Alvin Moon,&nbsp;Amanda Young","doi":"10.1007/s00023-023-01398-8","DOIUrl":"10.1007/s00023-023-01398-8","url":null,"abstract":"<div><p>We use cluster expansion methods to establish local the indistiguishability of the finite volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our estimates imply that the model satisfies local topological quantum order, and so, the spectral gap above the ground state is stable against local perturbations.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3603 - 3648"},"PeriodicalIF":1.4,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01398-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139072226","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
Local Hölder Stability in the Inverse Steklov and Calderón Problems for Radial Schrödinger Operators and Quantified Resonances 径向薛定谔算子和量化共振的反斯特克洛夫和卡尔德龙问题中的局部霍尔德稳定性
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-27 DOI: 10.1007/s00023-023-01391-1
Thierry Daudé, Niky Kamran, François Nicoleau
{"title":"Local Hölder Stability in the Inverse Steklov and Calderón Problems for Radial Schrödinger Operators and Quantified Resonances","authors":"Thierry Daudé,&nbsp;Niky Kamran,&nbsp;François Nicoleau","doi":"10.1007/s00023-023-01391-1","DOIUrl":"10.1007/s00023-023-01391-1","url":null,"abstract":"<div><p>We obtain Hölder stability estimates for the inverse Steklov and Calderón problems for Schrödinger operators corresponding to a special class of <span>(L^2)</span> radial potentials on the unit ball. These results provide an improvement on earlier logarithmic stability estimates obtained in Daudé et al. (J Geom Anal 31(2):1821–1854, 2021) in the case of the Schrödinger operators related to deformations of the closed Euclidean unit ball. The main tools involve: (i) A formula relating the difference of the Steklov spectra of the Schrödinger operators associated to the original and perturbed potential to the Laplace transform of the difference of the corresponding amplitude functions introduced by Simon (Ann Math 150:1029–1057, 1999) in his representation formula for the Weyl-Titchmarsh function, and (ii) a key moment stability estimate due to Still (J Approx Theory 45:26–54, 1985). It is noteworthy that with respect to the original Schrödinger operator, the type of perturbation being considered for the amplitude function amounts to the introduction of a finite number of negative eigenvalues and of a countable set of negative resonances which are quantified explicitly in terms of the eigenvalues of the Laplace-Beltrami operator on the boundary sphere.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 8","pages":"3805 - 3830"},"PeriodicalIF":1.4,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066228","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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