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(l^{2})-Decoupling and the Unconditional Uniqueness for the Boltzmann Equation (l^{2})-解耦和玻尔兹曼方程的无条件唯一性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05614-4
Xuwen Chen, Shunlin Shen, Zhifei Zhang
{"title":"(l^{2})-Decoupling and the Unconditional Uniqueness for the Boltzmann Equation","authors":"Xuwen Chen,&nbsp;Shunlin Shen,&nbsp;Zhifei Zhang","doi":"10.1007/s00220-026-05614-4","DOIUrl":"10.1007/s00220-026-05614-4","url":null,"abstract":"<div><p>We broaden the application of the <span>(l^{2})</span>-decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the <span>(mathbb {T}^d)</span> setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the <span>(mathbb {R}^d)</span> and <span>(mathbb {T}^d)</span> Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schrödinger equation.</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":"147796751","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
Simultaneous Replica-Symmetry Breaking for Vector Spin Glasses 矢量自旋玻璃的同步复制对称性破缺
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05589-2
Hong-Bin Chen, Jean-Christophe Mourrat
{"title":"Simultaneous Replica-Symmetry Breaking for Vector Spin Glasses","authors":"Hong-Bin Chen,&nbsp;Jean-Christophe Mourrat","doi":"10.1007/s00220-026-05589-2","DOIUrl":"10.1007/s00220-026-05589-2","url":null,"abstract":"<div><p>We consider mean-field vector spin glasses with possibly non-convex interactions. Up to a small perturbation of the parameters defining the model, the asymptotic behavior of the Gibbs measure is described in terms of a critical point of an explicit functional. In this paper, we study some properties of these critical points. Under modest assumptions ensuring that different types of spins interact, we show that the replica-symmetry-breaking structures of the different types of spins are in one-to-one correspondence with one another. For instance, if some type of spins displays one level of replica-symmetry breaking, then so do all the other types of spins. This extends the recent results of Bates and Sohn (Electron J Probab 27:1–75, 2022) and Bates and Sohn (Commun Math Phys 394:1101–1152, 2022) that were obtained in the case of multi-species spherical spin glasses with convex interactions.</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":"147796754","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
Self-dual Gauge Theory from the Top Down 自双规范理论自顶向下
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05606-4
Roland Bittleston, Kevin Costello, Keyou Zeng
{"title":"Self-dual Gauge Theory from the Top Down","authors":"Roland Bittleston,&nbsp;Kevin Costello,&nbsp;Keyou Zeng","doi":"10.1007/s00220-026-05606-4","DOIUrl":"10.1007/s00220-026-05606-4","url":null,"abstract":"<div><p>We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of 4<i>d</i> self-dual asymptotically flat backgrounds, and the large <i>N</i> limit of an independently defined 2<i>d</i> chiral defect CFT. Our construction goes via twisted holography for the type I topological string on a Calabi–Yau five-fold which fibres over twistor space. In particular, we show that single-trace operators of the 2<i>d</i> defect CFT are in bijection with states of the celestial chiral algebra. We match the operator products of these states with the collinear splitting amplitudes of the self-dual gauge theory up to one-loop. Assigning vacuum expectations to central operators in the boundary theory computes bulk amplitudes on self-dual backgrounds. We are able to extract form factors from these amplitudes, which we use to give a simple closed formula for certain <i>n</i>-point two-loop all + amplitudes in <span>(textrm{SU}(K) times textrm{SU}(R))</span> gauge theory coupled to bifundamental massless fermions.</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":"147796757","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
Global-in-Time Estimates for the 2D One-Phase Muskat Problem with Contact Points 具有接触点的二维单相Muskat问题的全局实时估计
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05633-1
Edoardo Bocchi, Ángel Castro, Francisco Gancedo
{"title":"Global-in-Time Estimates for the 2D One-Phase Muskat Problem with Contact Points","authors":"Edoardo Bocchi,&nbsp;Ángel Castro,&nbsp;Francisco Gancedo","doi":"10.1007/s00220-026-05633-1","DOIUrl":"10.1007/s00220-026-05633-1","url":null,"abstract":"<div><p>In this paper, we study the dynamics of a two-dimensional viscous fluid evolving through a porous medium or a Hele-Shaw cell, driven by gravity and surface tension. A key feature of this study is that the fluid is confined within a vessel with vertical walls and below a dry region. Consequently, the dynamics of the contact points between the vessel, the fluid and the dry region are inherently coupled with the surface evolution. A similar contact scenario was recently analyzed for more regular viscous flows, modeled by the Stokes (Guo and Tice, Arch Ration Mech Anal 227(2):767–854, 2018) and Navier–Stokes (Guo and Tice, J Eur Math Soc 26(4):1445–1557, 2024) equations. Here, we adopt the same framework but use the more singular Darcy’s law for modeling the flow. We prove global-in-time a priori estimates for solutions initially close to equilibrium. Taking advantage of the Neumann problem solved by the velocity potential, the analysis is carried out in non-weighted <span>(L^2)</span>-based Sobolev spaces and without imposing restrictions on the contact angles.</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/s00220-026-05633-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796671","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
On the Original Ulam’s Problem and Its Quantization 论原始乌兰问题及其量化
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05594-5
Changguang Dong, Jing Zhou
{"title":"On the Original Ulam’s Problem and Its Quantization","authors":"Changguang Dong,&nbsp;Jing Zhou","doi":"10.1007/s00220-026-05594-5","DOIUrl":"10.1007/s00220-026-05594-5","url":null,"abstract":"<div><p>We show that under general resonance the classical piecewise linear Fermi–Ulam accelerator behaves substantially different from its quantization, in the sense that the classical accelerator exhibits typical recurrence and non-escaping while the quantum version enjoys quadratic energy growth in general. We also describe a procedure to locate the escaping orbits, though exceptionally rare in the infinite-volume phase space, for the classical accelerators, which in particular include Ulam’s very original proposal and the linearly escaping orbits therein in the existing literature, and hence provide a complete (modulo a null set) answer to Ulam’s original question. For the quantum accelerators, we reveal under resonance the direct and explicit connection between the energy growth and the shape of the quasi-energy spectrum.</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":"147796673","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 Bisognano-Wichmann Property for Non-unitary Wightman Conformal Field Theories 非幺正Wightman共形场论的Bisognano-Wichmann性质
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05622-4
James E. Tener
{"title":"The Bisognano-Wichmann Property for Non-unitary Wightman Conformal Field Theories","authors":"James E. Tener","doi":"10.1007/s00220-026-05622-4","DOIUrl":"10.1007/s00220-026-05622-4","url":null,"abstract":"<div><p>The Bisognano-Wichmann and Haag duality properties for algebraic quantum field theories are often studied using the powerful tools of Tomita-Takesaki modular theory for nets of operator algebras. In this article, we study analogous properties of nets of algebras generated by smeared Wightman fields, for potentially non-unitary theories. In light of recent work constructing Wightman field theories for (non-unitary) Möbius vertex algebras, we obtain a broadly applicable non-unitary version of the Bisognano-Wichmann property. In this setting we do not have access to the traditional tools of Hilbert space functional analysis, like functional calculus. Instead, results analogous to those of Tomita-Takesaki theory are derived ‘by hand’ from the Wightman axioms. As an application, we demonstrate Haag duality for nets of smeared Wightman fields.</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/s00220-026-05622-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796680","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
High-Contrast Random Composites: Homogenisation Framework and Spectral Convergence 高对比度随机复合材料：均匀化框架和光谱收敛
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05601-9
Mikhail Cherdantsev, Kirill Cherednichenko, Igor Velčić
{"title":"High-Contrast Random Composites: Homogenisation Framework and Spectral Convergence","authors":"Mikhail Cherdantsev,&nbsp;Kirill Cherednichenko,&nbsp;Igor Velčić","doi":"10.1007/s00220-026-05601-9","DOIUrl":"10.1007/s00220-026-05601-9","url":null,"abstract":"<div><p>We develop a framework for multiscale analysis of elliptic operators with high-contrast random coefficients. For a general class of such operators, we provide a detailed spectral analysis of the corresponding homogenised limit operator. Under some lenient assumptions on the configuration of the random inclusions, we fully characterise the limit of the spectra of the high-contrast operators in question, which unlike in the periodic setting is shown to be different to the spectrum of the homogenised operator. Introducing a new notion of the <i>relevant limiting spectrum</i>, we describe the connection between these two sets.</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/s00220-026-05601-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796752","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
Pirogov–Sinai Theory for the Hard-Core Model Beyond Lattices 超晶格硬核模型的Pirogov-Sinai理论
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05623-3
Sarah Cannon, Tyler Helmuth, Will Perkins
{"title":"Pirogov–Sinai Theory for the Hard-Core Model Beyond Lattices","authors":"Sarah Cannon,&nbsp;Tyler Helmuth,&nbsp;Will Perkins","doi":"10.1007/s00220-026-05623-3","DOIUrl":"10.1007/s00220-026-05623-3","url":null,"abstract":"<div><p>Pirogov–Sinai theory is a well-developed method for understanding the low-temperature phase diagram of statistical mechanics models on lattices. Motivated by physical and algorithmic questions beyond the setting of lattices, we develop a combinatorially flexible version of Pirogov–Sinai theory for the hard-core model of independent sets on bipartite graphs. Our results illustrate that the main conclusions of Pirogov–Sinai theory can be obtained in significantly greater generality than that of <span>(mathbb {Z}^{d})</span>. The main ingredients in our generalization are combinatorial and involve developing appropriate definitions of contours based on the notion of cycle basis connectivity. This is inspired by works of Timár and Georgakopoulos–Panagiotis.</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/s00220-026-05623-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796674","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
Long-Time Dynamics of Small Solutions to 1d Cubic Nonlinear Schrödinger Equations with A Trapping Potential 具有捕获势的一维三次非线性Schrödinger方程小解的长时间动力学
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05645-x
Gong Chen
{"title":"Long-Time Dynamics of Small Solutions to 1d Cubic Nonlinear Schrödinger Equations with A Trapping Potential","authors":"Gong Chen","doi":"10.1007/s00220-026-05645-x","DOIUrl":"10.1007/s00220-026-05645-x","url":null,"abstract":"<div><p>In this paper, we analyze the long-time dynamics of small solutions to the 1<i>d</i> cubic nonlinear Schrödinger equation (NLS) with a trapping potential. We show that every small solution decomposes into a small solitary wave and a radiation term exhibiting modified scattering. Our analysis also establishes the long-time behavior of solutions to perturbations of the integrable cubic NLS in the presence of solitons.</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/s00220-026-05645-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796756","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
Nodal replication of Planar Random Waves 平面随机波的节点复制
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2026-05-02 DOI: 10.1007/s00220-026-05617-1
Loïc Thomassey, Raphaël Lachièze-Rey
{"title":"Nodal replication of Planar Random Waves","authors":"Loïc Thomassey,&nbsp;Raphaël Lachièze-Rey","doi":"10.1007/s00220-026-05617-1","DOIUrl":"10.1007/s00220-026-05617-1","url":null,"abstract":"<div><p>We study the <i>almost periods</i> of the eigenmodes of flat planar manifolds in the high energy limit. We prove in particular that the Gaussian Arithmetic Random Waves replicate almost identically at a scale at most <span>(ell _{n}:= n^{-frac{1}{2}}operatorname {exp}left( {mathcal {N}}_nright) )</span>, where <span>({mathcal {N}}_n)</span> is the number of ways <i>n</i> can be written as a sum of two squares. It provides a qualitative interpretation of the <i>full correlation phenomenon</i> of the nodal length, which is known to happen at scales larger than <span>(ell _{n}':= n^{-1/2}{mathcal {N}}_{n}^{A}.)</span> We provide also a heuristic with a toy model pleading that the minimal scale of replication should be closer to <span>(ell _{n}')</span> than <span>(ell _{n}.)</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":"147796850","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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