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Quantized Quiver Varieties and the Quantum Spin Ruijsenaars–Schneider Model 量子化微颤变体和量子自旋rujsenaars - schneider模型
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05595-4
Gleb Arutyunov, Lukas Hardi
{"title":"Quantized Quiver Varieties and the Quantum Spin Ruijsenaars–Schneider Model","authors":"Gleb Arutyunov,&nbsp;Lukas Hardi","doi":"10.1007/s00220-026-05595-4","DOIUrl":"10.1007/s00220-026-05595-4","url":null,"abstract":"<div><p>This paper tackles the long-standing problem of quantizing the rational spin Ruijsenaars–Schneider model originating in the work of Krichever and Zabrodin (Russ Math Surv 50:1101, 1995. arXiv:hep-th/9505039). We make use of the technique of quantum Hamiltonian reduction to construct a quantized quiver variety <span>(mathfrak {A}_{N,ell })</span>, which is simultaneously the algebra of quantum observables of the rational spin Ruijsenaars–Schneider model of <i>N</i> particles with <span>(ell )</span> spin polarizations. Inside this algebra, we find a loop algebra and Yangian of <span>(mathfrak {gl}_ell )</span> and conjecture that the algebra <span>(mathfrak {A}_{N,ell })</span> can be identified with a truncated Yangian of affine type <span>(A_{ell -1}^{(1)})</span>. Finally, we use the commutation relations inside <span>(mathfrak {A}_{N,ell })</span> to derive a difference equation for eigenstates of the lowest Hamiltonian that reproduces the known quantization of the spinless case when <span>(ell =1)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05595-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Rates for Maps and Flows in a Deterministic Multidimensional Weak Invariance Principle 确定性多维弱不变性原理中映射和流的速率
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05631-3
Nicolò Paviato
{"title":"Rates for Maps and Flows in a Deterministic Multidimensional Weak Invariance Principle","authors":"Nicolò Paviato","doi":"10.1007/s00220-026-05631-3","DOIUrl":"10.1007/s00220-026-05631-3","url":null,"abstract":"<div><p>We present the first rates of convergence to an <i>N</i>-dimensional Brownian motion when <span>(Nge 2)</span> for discrete and continuous time dynamical systems. Additionally, we provide the first rates for continuous time in any dimension. Our results hold for nonuniformly hyperbolic and expanding systems, such as Axiom A flows, suspensions over a Young tower with exponential tails, and some classes of intermittent solenoids.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Positive Energy Solutions in the Anisotropic Kepler Problem with Homogeneous Potential 具有齐次势的各向异性开普勒问题的正能量解
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05648-8
Guowei Yu
{"title":"Positive Energy Solutions in the Anisotropic Kepler Problem with Homogeneous Potential","authors":"Guowei Yu","doi":"10.1007/s00220-026-05648-8","DOIUrl":"10.1007/s00220-026-05648-8","url":null,"abstract":"<div><p>We study positive energy solutions of the anisotropic Kepler problem with homogeneous potential. First some asymptotic property of positive energy solutions is obtained, as time goes to infinity. Afterwards, we prove the existence of hyperbolic solutions with given initial configuration and asymptotic behavior, when time goes to positive or negative infinity, and in the planar case, the existence of bi-hyperbolic solutions with given asymptotic behaviors, when time goes to both positive and negative infinities, under various conditions.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Ribbon Categories of Weight Modules for Affine (mathfrak {sl}_{2}) at Admissible Levels 在可接受水平上的仿射权模的带状分类(mathfrak {sl}_{2})
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05636-y
Thomas Creutzig, Robert McRae, Jinwei Yang
{"title":"Ribbon Categories of Weight Modules for Affine (mathfrak {sl}_{2}) at Admissible Levels","authors":"Thomas Creutzig,&nbsp;Robert McRae,&nbsp;Jinwei Yang","doi":"10.1007/s00220-026-05636-y","DOIUrl":"10.1007/s00220-026-05636-y","url":null,"abstract":"<div><p>We show that the braided tensor category of finitely-generated weight modules for the simple affine vertex operator algebra <span>(L_k(mathfrak {sl}_2))</span> of <span>(mathfrak {sl}_2)</span> at any admissible level <i>k</i> is rigid and hence a braided ribbon category. The proof uses a recent result of the first two authors with Shimizu and Yadav on embedding a braided Grothendieck-Verdier category <span>(mathcal {C})</span> into the Drinfeld center of the category of modules for a suitable commutative algebra <i>A</i> in <span>(mathcal {C})</span>, in situations where the braided tensor category of local <i>A</i>-modules is rigid. Here, the commutative algebra <i>A</i> is Adamović’s inverse quantum Hamiltonian reduction of <span>(L_k(mathfrak {sl}_2))</span>, which is the simple rational Virasoro vertex operator algebra at central charge <span>(1-frac{6(k+1)^2}{k+2})</span> tensored with a half-lattice conformal vertex algebra. As a corollary, we also show that the category of finitely-generated weight modules for the <span>(N = 2)</span> super Virasoro vertex operator superalgebra at central charge <span>(-6ell -3)</span> is rigid for <span>(ell )</span> such that <span>((ell +1)(k+2) = 1)</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 a Classification of Steady Solutions to Two-Dimensional Euler Equations 二维欧拉方程稳定解的一类分类
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05632-2
Changfeng Gui, Chunjing Xie, Huan Xu
{"title":"On a Classification of Steady Solutions to Two-Dimensional Euler Equations","authors":"Changfeng Gui,&nbsp;Chunjing Xie,&nbsp;Huan Xu","doi":"10.1007/s00220-026-05632-2","DOIUrl":"10.1007/s00220-026-05632-2","url":null,"abstract":"<div><p>In this paper, we classify steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the whole plane must be the entire circle unless the flow is a parallel shear flow. In an infinitely long horizontal strip or the upper half-plane supplemented with slip boundary conditions, besides the two types of flows that appear in the whole space case, an additional class of steady flows exists for which the set of flow angles is either the upper or lower closed semicircle. This type of flows is proved to be the class of non-shear flows that have the least total curvature. An immediate consequence of our classification result is the structural stability of any shear flow with a convex shear profile. Our proof relies on the observation and analysis of some quantities related to the curvature of the streamlines.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Nonstandard Functional Central Limit Theorem for Nonuniformly Hyperbolic Dynamical Systems, Including Bunimovich Stadia 含Bunimovich体育场的非一致双曲动力系统的非标准泛函中心极限定理
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05649-7
Yuri Lima, Carlos Matheus, Ian Melbourne
{"title":"Nonstandard Functional Central Limit Theorem for Nonuniformly Hyperbolic Dynamical Systems, Including Bunimovich Stadia","authors":"Yuri Lima,&nbsp;Carlos Matheus,&nbsp;Ian Melbourne","doi":"10.1007/s00220-026-05649-7","DOIUrl":"10.1007/s00220-026-05649-7","url":null,"abstract":"<div><p>We consider a class of nonuniformly hyperbolic dynamical systems with a first return time satisfying a central limit theorem (CLT) with nonstandard normalisation <span>((nlog n)^{1/2})</span>. For such systems (both maps and flows) we show that it automatically follows that the functional central limit theorem or weak invariance principle (WIP) with normalisation <span>((nlog n)^{1/2})</span> holds for Hölder observables. Our approach streamlines certain arguments in the literature. Applications include various examples from billiards, geodesic flows and intermittent dynamical systems. In this way, we unify existing results as well as obtaining new results. In particular, we deduce the WIP with nonstandard normalisation for Bunimovich stadia as an immediate consequence of the corresponding CLT proved by Bálint &amp; Gouëzel.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 6","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05649-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Effective Quenched Linear Response for Random Dynamical Systems 随机动力系统的有效猝灭线性响应
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-04-28 DOI: 10.1007/s00220-026-05624-2
D. Dragičević, Y. Hafouta
{"title":"Effective Quenched Linear Response for Random Dynamical Systems","authors":"D. Dragičević,&nbsp;Y. Hafouta","doi":"10.1007/s00220-026-05624-2","DOIUrl":"10.1007/s00220-026-05624-2","url":null,"abstract":"<div><p>We prove “effective” linear response for certain classes of non-uniformly expanding random dynamical systems which are not necessarily composed in an i.i.d manner. In applications, the results are obtained for base maps with a sufficient amount of mixing. The fact that the rates are effective is then applied to obtain the differentiability of the variance in the CLT as a function of the parameter, as well as the annealed linear response. These two applications are beyond the reach of the linear response obtained in the general case, when all the random variables appearing in the bounds are only tempered. We also provide several wide examples of one-dimensional maps satisfying our conditions, as well as some higher-dimensional examples.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 Atiyah-Schmid Dimension Formula for Reductive Groups 约化群的Atiyah-Schmid维数公式
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-04-04 DOI: 10.1007/s00220-026-05619-z
Jun Yang
{"title":"The Atiyah-Schmid Dimension Formula for Reductive Groups","authors":"Jun Yang","doi":"10.1007/s00220-026-05619-z","DOIUrl":"10.1007/s00220-026-05619-z","url":null,"abstract":"<div><p>We give a generalization of the Atiyah-Schmid dimension formula for projective tempered representations. Then we prove the Atiyah-Schmid dimension formula for arithmetic subgroups of real reductive groups.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147614781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Hyperbolicity of Renormalization of Critical Quasicircle Maps 临界拟圆映射重整化的双曲性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-04-04 DOI: 10.1007/s00220-026-05580-x
Willie Rush Lim
{"title":"Hyperbolicity of Renormalization of Critical Quasicircle Maps","authors":"Willie Rush Lim","doi":"10.1007/s00220-026-05580-x","DOIUrl":"10.1007/s00220-026-05580-x","url":null,"abstract":"<div><p>There is a well developed renormalization theory of real analytic critical circle maps by de Faria, de Melo, and Yampolsky. In this paper, we extend Yampolsky’s result on the hyperbolicity of renormalization periodic points to a larger class of dynamical objects, namely critical quasicircle maps, i.e. analytic self-homeomorphisms of a quasicircle with a single critical point. Unlike critical circle maps, the inner and outer criticalities of critical quasicircle maps can be distinct. We develop a compact analytic renormalization operator called “Corona Renormalization“ with a hyperbolic fixed point whose stable manifold has codimension one and consists of critical quasicircle maps of the same criticality and periodic type rotation number. Our proof is an adaptation of Pacman Renormalization Theory for Siegel disks as well as rigidity results on the escaping dynamics of transcendental entire functions.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147612875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Cups and Gates I: Cohomology Invariants and Logical Quantum Operations Cups与Gates I：上同调不变量与逻辑量子运算
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-04-04 DOI: 10.1007/s00220-026-05570-z
Nikolas P. Breuckmann, Margarita Davydova, Jens N. Eberhardt, Nathanan Tantivasadakarn
{"title":"Cups and Gates I: Cohomology Invariants and Logical Quantum Operations","authors":"Nikolas P. Breuckmann,&nbsp;Margarita Davydova,&nbsp;Jens N. Eberhardt,&nbsp;Nathanan Tantivasadakarn","doi":"10.1007/s00220-026-05570-z","DOIUrl":"10.1007/s00220-026-05570-z","url":null,"abstract":"<div><p>We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that <i>cohomology invariants</i> naturally give rise to diagonal logical gates. We show that such invariants exist if the quantum code has a structure that relaxes certain properties of a differential graded algebra. We show how to equip quantum codes with such a structure by defining <i>cup products</i> on CSS codes. The logical gates obtained from this approach can be implemented by a constant-depth unitary circuit. In particular, we construct a <span>(Lambda )</span>-fold cup product that can produce a logical operator in the <span>(Lambda )</span>-th level of the Clifford hierarchy on <span>(Lambda )</span> copies of the same quantum code, which we call the <i>copy-cup gate</i>. For any desired <span>(Lambda )</span>, we can construct several families of quantum codes that support gates in the <span>(Lambda )</span>-th level with various asymptotic code parameters.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"407 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-026-05570-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147614784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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