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Communications in Mathematical Physics最新文献

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Correction to: Couplings via Comparison Principle and Exponential Ergodicity of SPDEs in the Hypoelliptic Setting 修正：通过比较原理的耦合和准椭圆环境下spde的指数遍历性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05424-0
Oleg Butkovsky, Michael Scheutzow
{"title":"Correction to: Couplings via Comparison Principle and Exponential Ergodicity of SPDEs in the Hypoelliptic Setting","authors":"Oleg Butkovsky, Michael Scheutzow","doi":"10.1007/s00220-025-05424-0","DOIUrl":"10.1007/s00220-025-05424-0","url":null,"abstract":"","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05424-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923132","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
Stochastic Quantization of the Three-Dimensional Polymer Measure via Dirichlet Form Method 三维聚合物测量的狄利克雷形式随机量化方法
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05419-x
Sergio Albeverio, Seiichiro Kusuoka, Song Liang, Makoto Nakashima
{"title":"Stochastic Quantization of the Three-Dimensional Polymer Measure via Dirichlet Form Method","authors":"Sergio Albeverio,&nbsp;Seiichiro Kusuoka,&nbsp;Song Liang,&nbsp;Makoto Nakashima","doi":"10.1007/s00220-025-05419-x","DOIUrl":"10.1007/s00220-025-05419-x","url":null,"abstract":"<div><p>We prove that there exists a diffusion process whose invariant measure is the three-dimensional polymer measure <span>(nu _lambda )</span> for all <span>(lambda &gt;0)</span>. We follow in part a previous incomplete unpublished work of the first named author with M. Röckner and X. Y. Zhou (Stochastic quantization of the three-dimensional polymer measure, 1996). For the construction of <span>(nu _lambda )</span> we rely on previous work by J. Westwater, E. Bolthausen and X.Y. Zhou. Using <span>(nu _lambda )</span>, the diffusion is constructed by means of the theory of Dirichlet forms on infinite-dimensional state spaces. The closability of the appropriate pre-Dirichlet form which is of gradient type is proven, by using a general closability result by the first named author and Röckner (Probab Theory Related Fields 83(3):405–434, 1989). This result does not require an integration by parts formula (which does not even hold for the two-dimensional polymer measure <span>(nu _lambda )</span>) but requires the quasi-invariance of <span>(nu _lambda )</span> along a basis of vectors in the classical Cameron-Martin space such that the Radon-Nikodym derivatives have versions which form a continuous process.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05419-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923046","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
Central Limit Theorem for Multi-Point Functions of the 2D Discrete Gaussian Model at High Temperature 高温下二维离散高斯模型多点函数的中心极限定理
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05396-1
Jiwoon Park
{"title":"Central Limit Theorem for Multi-Point Functions of the 2D Discrete Gaussian Model at High Temperature","authors":"Jiwoon Park","doi":"10.1007/s00220-025-05396-1","DOIUrl":"10.1007/s00220-025-05396-1","url":null,"abstract":"<div><p>We study microscopic observables of the Discrete Gaussian model (i.e., the Gaussian free field restricted to take integer values) at high temperature using the renormalisation group method. In particular, we show the central limit theorem for the two-point function of the Discrete Gaussian model by computing the asymptotic of the moment generating function <span>(big langle e^{{mathcalligra {z}}(sigma (0) - sigma (y))} big rangle _{beta , {mathbb {Z}}^2}^{operatorname {DG}})</span> for <span>({mathcalligra {z}}in {mathbb {C}})</span> sufficiently small. The method we use has direct connection with the multi-scale polymer expansion used in Bauerschmidt et al. (Ann Probab 52(4):1253–1359, 2024, Ann Probab 52(4):1360–1398, 2024), where it was used to study the scaling limit of the Discrete Gaussian model. The method also applies to multi-point functions and lattice models of sine-Gordon type studied in Fröhlich and Spencer (Commun Math Phys 81(4): 527–602, 1981).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923135","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
Testing Quantum Satisfiability 测试量子可满足性
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05377-4
Ashley Montanaro, Changpeng Shao, Dominic Verdon
{"title":"Testing Quantum Satisfiability","authors":"Ashley Montanaro,&nbsp;Changpeng Shao,&nbsp;Dominic Verdon","doi":"10.1007/s00220-025-05377-4","DOIUrl":"10.1007/s00220-025-05377-4","url":null,"abstract":"<div><p>Quantum <i>k</i>-SAT (the problem of determining whether a <i>k</i>-local Hamiltonian is frustration-free) is known to be QMA<span>(_1)</span>-complete for <span>(kge 3)</span>, and hence likely hard for quantum computers to solve. Building on a classical result of Alon and Shapira, we show that quantum <i>k</i>-SAT can be solved in randomised polynomial time given the ‘property testing’ promise that the instance is either satisfiable (by any state) or far from satisfiable by a product state; by ‘far from satisfiable by a product state’ we mean that <span>(epsilon n^k)</span> constraints must be removed before a product state solution exists, for some fixed <span>(epsilon &gt;0)</span>. The proof has two steps: we first show that for a satisfiable instance of quantum <i>k</i>-SAT, most subproblems on a constant number of qubits are satisfiable by a product state. We then show that for an instance of quantum <i>k</i>-SAT which is far from satisfiable by a product state, most subproblems are unsatisfiable by a product state. Given the promise, quantum <i>k</i>-SAT may therefore be solved by checking satisfiability by a product state on randomly chosen subsystems of constant size.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05377-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923051","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
Fourth Order Saint-Venant Inequalities: Maximizing Compliance and Mean Deflection Among Clamped Plates 四阶圣维南不等式：最大化夹持板间的柔度和平均挠度
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05439-7
Mark S. Ashbaugh, Dorin Bucur, Richard S. Laugesen, Roméo Leylekian
{"title":"Fourth Order Saint-Venant Inequalities: Maximizing Compliance and Mean Deflection Among Clamped Plates","authors":"Mark S. Ashbaugh,&nbsp;Dorin Bucur,&nbsp;Richard S. Laugesen,&nbsp;Roméo Leylekian","doi":"10.1007/s00220-025-05439-7","DOIUrl":"10.1007/s00220-025-05439-7","url":null,"abstract":"<div><p>We prove a fourth order analogue of the Saint-Venant inequality: the mean deflection of a clamped plate under uniform transverse load is maximal for the ball, among plates of prescribed volume in any dimension of space. The method works in the Euclidean space, the hyperbolic space, and the sphere. Similar results for clamped plates under small compression and for the compliance under non-uniform loads are proved to hold in two dimensional Euclidean space, with the higher dimensional and curved cases of those problems left open.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05439-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923105","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
Spacelike Initial Data for Black Hole Stability 黑洞稳定性的类空间初始数据
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05416-0
Allen Juntao Fang, Jérémie Szeftel, Arthur Touati
{"title":"Spacelike Initial Data for Black Hole Stability","authors":"Allen Juntao Fang,&nbsp;Jérémie Szeftel,&nbsp;Arthur Touati","doi":"10.1007/s00220-025-05416-0","DOIUrl":"10.1007/s00220-025-05416-0","url":null,"abstract":"<div><p>We construct initial data suitable for the Kerr stability conjecture, that is, solutions to the constraint equations on a spacelike hypersurface with boundary entering the black hole horizon that are arbitrarily decaying perturbations of a Kerr initial data set. This results from a more general perturbative construction on any asymptotically flat initial data set with <span>(r^{-1})</span> fall-off and the topology of <span>(mathbb {R}^3setminus {r&lt;1})</span> enjoying some analyticity near and at the boundary. In particular, we design a suitable mixed boundary condition for the elliptic operator of the conformal method in order to exclude the Killing initial data sets (KIDS).</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923134","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
Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis 通过量子傅立叶分析测试稳定器和魔术熵
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05421-3
Kaifeng Bu, Weichen Gu, Arthur Jaffe
{"title":"Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis","authors":"Kaifeng Bu,&nbsp;Weichen Gu,&nbsp;Arthur Jaffe","doi":"10.1007/s00220-025-05421-3","DOIUrl":"10.1007/s00220-025-05421-3","url":null,"abstract":"<div><p>Quantum Fourier analysis is an important topic in mathematical physics. We introduce a systematic protocol for testing and measuring “magic” in quantum states and gates, using a quantum Fourier approach. Magic, as a quantum resource, is necessary to achieve a quantum advantage in computation. Our protocols are based on quantum convolutions and swap tests, implemented via quantum circuits. We describe this for both qubit and qudit systems. Our quantum Fourier approach offers a unified method to quantify magic, in stabilizer circuits, as well as in matchgate and bosonic Gaussian circuits.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923133","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
Anosov Vector Fields and Fried Sections 阿诺索夫矢量场和油炸截面
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05400-8
Jean-Michel Bismut, Shu Shen
{"title":"Anosov Vector Fields and Fried Sections","authors":"Jean-Michel Bismut,&nbsp;Shu Shen","doi":"10.1007/s00220-025-05400-8","DOIUrl":"10.1007/s00220-025-05400-8","url":null,"abstract":"<div><p>The purpose of this paper is to prove that if <i>Y</i> is a compact manifold, if <i>Z</i> is an Anosov vector field on <i>Y</i>, and if <i>F</i> is a flat vector bundle, there is a corresponding canonical nonzero section <span>(tau _{nu }left( i_{Z}right) )</span> of the determinant line <span>(nu =det Hleft( Y,Fright) )</span>. In families, this section is <span>(C^{1})</span> with respect to the canonical smooth structure on <span>(nu )</span>. When <i>F</i> is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on <span>(nu )</span>.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05400-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923052","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
Phase Transition for Discrete Nonlinear Schrödinger Equation in Three and Higher Dimensions 三维及高维离散非线性Schrödinger方程的相变
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05408-0
Partha S. Dey, Kay Kirkpatrick, Kesav Krishnan
{"title":"Phase Transition for Discrete Nonlinear Schrödinger Equation in Three and Higher Dimensions","authors":"Partha S. Dey,&nbsp;Kay Kirkpatrick,&nbsp;Kesav Krishnan","doi":"10.1007/s00220-025-05408-0","DOIUrl":"10.1007/s00220-025-05408-0","url":null,"abstract":"<div><p>We analyze the thermodynamics of the focusing discrete nonlinear Schrödinger equation in dimensions <span>(dgeqslant 3)</span> with general power nonlinearity <span>(p&gt;1)</span>, under a model with two parameters that are inverse temperature and the nonlinearity strength. We prove the existence of the limiting free energy of the associated invariant Gibbs measure and analyze the phase diagram for general <i>d</i>, <i>p</i>. We prove the existence of a continuous phase transition curve that divides the parametric plane into two regions involving the appearance or non-appearance of solitons. Appropriate upper and lower bounds for the curve are constructed that match the result in Chatterjee and Kirkpatrick (Commun Pure Appl Math 65(5):727–757, 2012) a one-sided asymptotic limit. We also look at the typical behavior of a function from the Gibbs measure for parts of the phase diagram.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923088","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
Small-Amplitude Finite-Depth Stokes Waves are Transversally Unstable 小振幅有限深度斯托克斯波是横向不稳定的
IF 2.6 1区 物理与天体物理
Communications in Mathematical Physics Pub Date : 2025-09-01 DOI: 10.1007/s00220-025-05428-w
Ziang Jiao, L. Miguel Rodrigues, Changzhen Sun, Zhao Yang
{"title":"Small-Amplitude Finite-Depth Stokes Waves are Transversally Unstable","authors":"Ziang Jiao,&nbsp;L. Miguel Rodrigues,&nbsp;Changzhen Sun,&nbsp;Zhao Yang","doi":"10.1007/s00220-025-05428-w","DOIUrl":"10.1007/s00220-025-05428-w","url":null,"abstract":"<div><p>We prove that all irrotational planar periodic traveling waves of sufficiently small-amplitude are spectrally unstable as solutions to three-dimensional inviscid finite-depth gravity water-waves equations.\u0000</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 10","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144923106","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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