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Local Statistics in Normal Matrix Models with Merging Singularity 具有合并奇异点的正态矩阵模型的局部统计量
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05316-3
Torben Krüger, Seung-Yeop Lee, Meng Yang
{"title":"Local Statistics in Normal Matrix Models with Merging Singularity","authors":"Torben Krüger,&nbsp;Seung-Yeop Lee,&nbsp;Meng Yang","doi":"10.1007/s00220-025-05316-3","DOIUrl":"10.1007/s00220-025-05316-3","url":null,"abstract":"<div><p>We study the normal matrix model, also known as the two-dimensional one-component plasma at a specific temperature, with merging singularity. As the number <i>n</i> of particles tends to infinity we obtain the limiting local correlation kernel at the singularity, which is related to the parametrix of the Painlevé II equation. The two main tools are Riemann–Hilbert problems and the generalized Christoffel–Darboux identity. The correlation kernel exhibits a novel anisotropic scaling behavior, where the corresponding spacing scale of particles is <span>(n^{-1/3})</span> in the direction of merging and <span>(n^{-1/2})</span> in the perpendicular direction. In the vicinity at different distances to the merging singularity we also observe Ginibre bulk and edge statistics, as well as the sine-kernel and the erfc-type kernel (a.k.a. the Faddeeva plasma kernel).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913837","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
Conformal Blocks on Smoothings via Mode Transition Algebras 经由模态转换代数的光滑上的共形块
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05237-1
Chiara Damiolini, Angela Gibney, Daniel Krashen
{"title":"Conformal Blocks on Smoothings via Mode Transition Algebras","authors":"Chiara Damiolini,&nbsp;Angela Gibney,&nbsp;Daniel Krashen","doi":"10.1007/s00220-025-05237-1","DOIUrl":"10.1007/s00220-025-05237-1","url":null,"abstract":"<div><p>Here we introduce a series of associative algebras attached to a vertex operator algebra <i>V</i> of CFT type, called mode transition algebras, and show they reflect both algebraic properties of <i>V</i> and geometric constructions on moduli of curves. Pointed and coordinatized curves, labeled by admissible <i>V</i>-modules, give rise to sheaves of coinvariants. We show that if the mode transition algebras admit multiplicative identities satisfying certain natural properties (called strong identity elements), these sheaves deform as wanted on families of curves with nodes. This provides new contexts in which coherent sheaves of coinvariants form vector bundles. We also show that mode transition algebras carry information about higher level Zhu algebras and generalized Verma modules. To illustrate, we explicitly describe the higher level Zhu algebras of the Heisenberg vertex operator algebra, proving a conjecture of Addabbo–Barron.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05237-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913874","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
Universality of Outliers in Weakly Confined Coulomb-Type Systems 弱约束库仑型系统异常值的普遍性
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05293-7
Raphael Butez, David García-Zelada, Alon Nishry, Aron Wennman
{"title":"Universality of Outliers in Weakly Confined Coulomb-Type Systems","authors":"Raphael Butez,&nbsp;David García-Zelada,&nbsp;Alon Nishry,&nbsp;Aron Wennman","doi":"10.1007/s00220-025-05293-7","DOIUrl":"10.1007/s00220-025-05293-7","url":null,"abstract":"<div><p>This work concerns <i>weakly confined</i> particle systems in the plane, characterized by a large number of outliers away from a <i>droplet</i> where the bulk of the particles accumulate in the many-particle limit. We consider two main examples: determinantal Coulomb gases confined by a regular background, and a class of random polynomials. We observe that the limiting outlier process only depends on the <i>shape</i> of the uncharged region containing them, and the global net excess charge. In particular, for a determinantal Coulomb gas confined by a sufficiently regular background measure, the outliers in a simply connected uncharged region converge to the corresponding Bergman point process. For a finitely connected uncharged region <span>(Omega )</span>, we give an explicit description of the possible limiting outlier processes. Moreover, the outliers in different uncharged regions are asymptotically independent, even if the regions have common boundary points. The latter result is a manifestation of screening properties of the particle system.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913835","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 Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model Ising模型图形表示的一致偶子图及其与相变的联系
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05297-3
Ulrik Thinggaard Hansen, Boris Kjær, Frederik Ravn Klausen
{"title":"The Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model","authors":"Ulrik Thinggaard Hansen,&nbsp;Boris Kjær,&nbsp;Frederik Ravn Klausen","doi":"10.1007/s00220-025-05297-3","DOIUrl":"10.1007/s00220-025-05297-3","url":null,"abstract":"<div><p>The uniform even subgraph is intimately related to the Ising model, the random-cluster model, the random current model, and the loop <span>(textrm{O})</span>(1) model. In this paper, we first prove that the uniform even subgraph of <span>(mathbb {Z}^d)</span> percolates for <span>(d ge 2)</span> using its characterisation as the Haar measure on the group of even graphs. We then tighten the result by showing that the loop <span>(textrm{O})</span>(1) model on <span>(mathbb {Z}^d)</span> percolates for <span>(d ge 2)</span> for edge-weights <i>x</i> lying in some interval <span>((1-varepsilon ,1])</span>. Finally, our main theorem is that the loop <span>(textrm{O})</span>(1) model and random current models corresponding to a supercritical Ising model are always at least critical, in the sense that their two-point correlation functions decay at most polynomially and the expected cluster sizes are infinite.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05297-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913875","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
Perturbative Diagonalization and Spectral Gaps of Quasiperiodic Operators on (ell ^2(mathbb Z^d)) with Monotone Potentials (ell ^2(mathbb Z^d))上具有单调势的拟周期算子的微扰对角化和谱隙
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05280-y
Ilya Kachkovskiy, Leonid Parnovski, Roman Shterenberg
{"title":"Perturbative Diagonalization and Spectral Gaps of Quasiperiodic Operators on (ell ^2(mathbb Z^d)) with Monotone Potentials","authors":"Ilya Kachkovskiy,&nbsp;Leonid Parnovski,&nbsp;Roman Shterenberg","doi":"10.1007/s00220-025-05280-y","DOIUrl":"10.1007/s00220-025-05280-y","url":null,"abstract":"<div><p>We obtain a perturbative proof of localization for quasiperiodic operators on <span>(ell ^2(mathbb Z^d))</span> with one-dimensional phase space and monotone sampling functions, in the regime of small hopping. The proof is based on an iterative scheme which can be considered as a local (in the energy and the phase) and convergent version of KAM-type diagonalization, whose result is a covariant family of uniformly localized eigenvalues and eigenvectors. We also prove that the spectra of such operators contain infinitely many gaps.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05280-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913831","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
Affine (mathcal{W})-Algebras and Miura Maps from 3d (mathcal {N}text {=},4) Non-Abelian Quiver Gauge Theories 仿射(mathcal{W}) -代数和三维的Miura映射(mathcal {N}text {=},4)非阿贝尔颤振规范理论
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05277-7
Ioana Coman, Myungbo Shim, Masahito Yamazaki, Yehao Zhou
{"title":"Affine (mathcal{W})-Algebras and Miura Maps from 3d (mathcal {N}text {=},4) Non-Abelian Quiver Gauge Theories","authors":"Ioana Coman,&nbsp;Myungbo Shim,&nbsp;Masahito Yamazaki,&nbsp;Yehao Zhou","doi":"10.1007/s00220-025-05277-7","DOIUrl":"10.1007/s00220-025-05277-7","url":null,"abstract":"<div><p>We study Vertex Operator Algebras (VOAs) obtained from the H-twist of 3d <span>(mathcal {N}=4)</span> linear quiver gauge theories. We find that H-twisted VOAs can be regarded as the “chiralization” of the extended Higgs branch: many of the ingredients of the Higgs branch are naturally “uplifted” into the VOAs, while conversely the Higgs branch can be recovered as the associated variety of the VOA. We also discuss the connection of our VOA with affine <span>(mathcal {W})</span>-algebras. For example, we construct an explicit homomorphism from an affine <span>(mathcal {W})</span>-algebra <span>(mathcal{W}^{-n+1}(mathfrak {gl}_n,f_{min }))</span> into the H-twisted VOA for <span>(T^{[2,1^{n-2}]}_{[1^n]}[textrm{SU}(n)])</span> theories. Motivated by the relation with affine <span>(mathcal {W})</span>-algebras, we introduce a reduction procedure for the quiver diagram, and use this to give an algorithm to systematically construct novel free-field realizations for VOAs associated with general linear quivers.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913833","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
Time-Dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence 基于Magnus展开的时变哈密顿模拟：算法与超收敛
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-07 DOI: 10.1007/s00220-025-05314-5
Di Fang, Diyi Liu, Rahul Sarkar
{"title":"Time-Dependent Hamiltonian Simulation via Magnus Expansion: Algorithm and Superconvergence","authors":"Di Fang,&nbsp;Diyi Liu,&nbsp;Rahul Sarkar","doi":"10.1007/s00220-025-05314-5","DOIUrl":"10.1007/s00220-025-05314-5","url":null,"abstract":"<div><p>Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is desired. We introduce a new time-dependent Hamiltonian simulation algorithm based on the Magnus expansion that exhibits both features. Importantly, when applied to unbounded Hamiltonian simulation in the interaction picture, we prove that the commutator in the second-order algorithm leads to a surprising fourth-order superconvergence, with an error preconstant independent of the number of spatial grids. This extends the qHOP algorithm (An et al. in Quantum 6:690, 2022) based on first-order Magnus expansion, and the proof of superconvergence is based on semiclassical analysis that is of independent interest.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 6","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913836","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
Energy-Limited Quantum Dynamics 能量有限的量子动力学
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1007/s00220-025-05282-w
Lauritz van Luijk
{"title":"Energy-Limited Quantum Dynamics","authors":"Lauritz van Luijk","doi":"10.1007/s00220-025-05282-w","DOIUrl":"10.1007/s00220-025-05282-w","url":null,"abstract":"<div><p>We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, only introduce a finite amount of energy to the system, and continuous-time dynamics only increase the energy gradually over time. We systematically study such “energy-limited” channels and dynamics. For Markovian dynamics, energy-limitedness is equivalent to a single operator inequality in the Heisenberg picture. We observe new submultiplicativity inequalities for the energy-constrained diamond and operator norm. As an application, we derive new state-dependent continuity bounds for quantum speed limits.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05282-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904679","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
Remarks on the (mathbb {Z}/p) Dijkgraaf-Witten Invariants of 3D Mapping Tori 三维映射环面的(mathbb {Z}/p) Dijkgraaf-Witten不变量的注释
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-05 DOI: 10.1007/s00220-025-05279-5
William Chen, Alex Kontorovich, Shehryar Sikander
{"title":"Remarks on the (mathbb {Z}/p) Dijkgraaf-Witten Invariants of 3D Mapping Tori","authors":"William Chen,&nbsp;Alex Kontorovich,&nbsp;Shehryar Sikander","doi":"10.1007/s00220-025-05279-5","DOIUrl":"10.1007/s00220-025-05279-5","url":null,"abstract":"<div><p>We make some remarks on the <span>(mathbb {Z}/p)</span> Dijkgraaf-Witten invariants of 3D mapping tori and determine the asymptotic behavior of their sum over all diffeomorphism classes of 3D mapping tori of genus one.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904680","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
Interlacing Triangles, Schubert Puzzles, and Graph Colorings 交错三角形，舒伯特谜题和图形着色
IF 2.2 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-05-03 DOI: 10.1007/s00220-025-05312-7
Christian Gaetz, Yibo Gao
{"title":"Interlacing Triangles, Schubert Puzzles, and Graph Colorings","authors":"Christian Gaetz,&nbsp;Yibo Gao","doi":"10.1007/s00220-025-05312-7","DOIUrl":"10.1007/s00220-025-05312-7","url":null,"abstract":"<div><p>We show that <i>interlacing triangular arrays</i>, introduced by Aggarwal–Borodin–Wheeler to study certain probability measures, can be used to compute structure constants for multiplying Schubert classes in the <i>K</i>-theory of Grassmannians, in the cohomology of their cotangent bundles, and in the cohomology of partial flag varieties. Our results are achieved by establishing a splitting lemma, allowing for interlacing triangular arrays of high rank to be decomposed into arrays of lower rank, and by constructing a bijection between interlacing triangular arrays of rank 3 with certain proper vertex colorings of the triangular grid graph that factors through generalizations of Knutson–Tao puzzles. Along the way, we prove one enumerative conjecture of Aggarwal–Borodin–Wheeler and disprove another.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900833","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
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