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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
(L^2)-Decay Rate for Special Solutions to Critical Dissipative Nonlinear Schrödinger Equations 临界耗散非线性薛定谔方程特殊解的 $L^2$$ - 衰变率
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-26 DOI: 10.1007/s00023-023-01403-0
Takuya Sato
{"title":"(L^2)-Decay Rate for Special Solutions to Critical Dissipative Nonlinear Schrödinger Equations","authors":"Takuya Sato","doi":"10.1007/s00023-023-01403-0","DOIUrl":"10.1007/s00023-023-01403-0","url":null,"abstract":"<div><p>We consider the Cauchy problem of one-dimensional dissipative nonlinear Schrödinger equations with a critical power nonlinearity. In the previous work, Ogawa–Sato (Nonlinear Differ Equ Appl 27:18, 2020) showed the upper <span>(L^2)</span>-decay estimate of dissipative solutions in the analytic class. In this paper, we show that <span>(L^2)</span>-decay rate obtained in the previous work is optimal for special solutions by obtaining the lower <span>(L^2)</span>-decay estimate.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 2","pages":"1693 - 1709"},"PeriodicalIF":1.4,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139057749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rademacher Expansion of a Siegel Modular Form for ({{mathcal {N}}}= 4) Counting 计算 $${{mathcal {N}}= 4$ 的西格尔模形式的拉德马赫展开
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-25 DOI: 10.1007/s00023-023-01400-3
Gabriel Lopes Cardoso, Suresh Nampuri, Martí Rosselló
{"title":"Rademacher Expansion of a Siegel Modular Form for ({{mathcal {N}}}= 4) Counting","authors":"Gabriel Lopes Cardoso,&nbsp;Suresh Nampuri,&nbsp;Martí Rosselló","doi":"10.1007/s00023-023-01400-3","DOIUrl":"10.1007/s00023-023-01400-3","url":null,"abstract":"<div><p>The degeneracies of 1/4 BPS states with unit torsion in heterotic string theory compactified on a six torus are given in terms of the Fourier coefficients of the reciprocal of the Igusa cusp Siegel modular form <span>(Phi _{10})</span> of weight 10. We use the symplectic symmetries of the latter to construct a fine-grained Rademacher-type expansion which expresses these BPS degeneracies as a regularized sum over residues of the poles of <span>(1/Phi _{10})</span>. The construction uses two distinct <span>(textrm{SL}(2, {mathbb {Z}}))</span> subgroups of <span>(textrm{Sp}(2, {mathbb {Z}}))</span> which encode multiplier systems, Kloosterman sums and Eichler integrals appearing therein. Additionally, it shows how the polar data are explicitly built from the Fourier coefficients of <span>(1/eta ^{24})</span> by means of a continued fraction structure.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 9","pages":"4065 - 4120"},"PeriodicalIF":1.4,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-023-01400-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139036938","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 Rotation Number for Almost Periodic Potentials with Jump Discontinuities and (delta )-Interactions 具有跃迁不连续和 $$delta $$ 相互作用的几乎周期势的旋转数
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2023-12-22 DOI: 10.1007/s00023-023-01404-z
David Damanik, Meirong Zhang, Zhe Zhou
{"title":"The Rotation Number for Almost Periodic Potentials with Jump Discontinuities and (delta )-Interactions","authors":"David Damanik,&nbsp;Meirong Zhang,&nbsp;Zhe Zhou","doi":"10.1007/s00023-023-01404-z","DOIUrl":"10.1007/s00023-023-01404-z","url":null,"abstract":"<div><p>We consider one-dimensional Schrödinger operators with generalized almost periodic potentials with jump discontinuities and <span>(delta )</span>-interactions. For operators of this kind, we introduce a rotation number in the spirit of Johnson and Moser. To do this, we introduce the concept of almost periodicity at a rather general level, and then the almost periodic function with jump discontinuities and <span>(delta )</span>-interactions as an application.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 2","pages":"1359 - 1397"},"PeriodicalIF":1.4,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946979","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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