Communications in Mathematical Physics最新文献

Rewriting History in Integrable Stochastic Particle Systems 在可积分随机粒子系统中重写历史

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-29 DOI: 10.1007/s00220-024-05189-y

Leonid Petrov, Axel Saenz

{"title":"Rewriting History in Integrable Stochastic Particle Systems","authors":"Leonid Petrov, Axel Saenz","doi":"10.1007/s00220-024-05189-y","DOIUrl":"10.1007/s00220-024-05189-y","url":null,"abstract":"<div>Many integrable stochastic particle systems in one space dimension (such as TASEP—Totally Asymmetric Simple Exclusion Process—and its q-deformation, the q-TASEP) remain integrable if we equip each particle with its own speed parameter. In this work, we present intertwining relations between Markov transition operators of particle systems which differ by a permutation of the speed parameters. These relations generalize our previous works (Petrov and Saenz in Probab Theory Relat Fields 182:481–530, 2022), (Petrov in SIGMA 17(021):34, 2021), but here we employ a novel approach based on the Yang-Baxter equation for the higher spin stochastic six vertex model. Our intertwiners are Markov transition operators, which leads to interesting probabilistic consequences. First, we obtain a new Lax-type differential equation for the Markov transition semigroups of homogeneous, continuous-time versions of our particle systems. Our Lax equation encodes the time evolution of multipoint observables of the q-TASEP and TASEP in a unified way, which may be of interest for the asymptotic analysis of multipoint observables of these systems. Second, we show that our intertwining relations lead to couplings between probability measures on trajectories of particle systems which differ by a permutation of the speed parameters. The conditional distribution for such a coupling is realized as a “rewriting history” random walk which randomly resamples the trajectory of a particle in a chamber determined by the trajectories of the neighboring particles. As a byproduct, we construct a new coupling for standard Poisson processes on the positive real half-line with different rates.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05189-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142736968","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

Hidden ({text {Sp}}(1))-Symmetry and Brane Quantization on HyperKähler Manifolds 隐藏的（{text {Sp}}(1)）对称性和超凯勒方程上的布兰量子化

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-23 DOI: 10.1007/s00220-024-05135-y

NaiChung Conan Leung, YuTung Yau

引用次数: 0

SU(2)-Equivariant Quantum Channels: Semiclassical Analysis SU(2)-Equivariant Quantum Channels：半经典分析

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-23 DOI: 10.1007/s00220-024-05178-1

Tommaso Aschieri, Błażej Ruba, Jan Philip Solovej

引用次数: 0

5d 2-Chern-Simons Theory and 3d Integrable Field Theories 5d 2-Chern-Simons 理论和 3d 可积分场理论

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-21 DOI: 10.1007/s00220-024-05170-9

Alexander Schenkel, Benoît Vicedo

{"title":"5d 2-Chern-Simons Theory and 3d Integrable Field Theories","authors":"Alexander Schenkel, Benoît Vicedo","doi":"10.1007/s00220-024-05170-9","DOIUrl":"10.1007/s00220-024-05170-9","url":null,"abstract":"<div>The 4-dimensional semi-holomorphic Chern-Simons theory of Costello and Yamazaki provides a gauge-theoretic origin for the Lax connection of 2-dimensional integrable field theories. The purpose of this paper is to extend this framework to the setting of 3-dimensional integrable field theories by considering a 5-dimensional semi-holomorphic higher Chern-Simons theory for a higher connection (A, B) on (mathbb {R}^3 times mathbb {C}P^1). The input data for this theory are the choice of a meromorphic 1-form (omega ) on (mathbb {C}P^1) and a strict Lie 2-group with cyclic structure on its underlying Lie 2-algebra. Integrable field theories on (mathbb {R}^3) are constructed by imposing suitable boundary conditions on the connection (A, B) at the 3-dimensional defects located at the poles of (omega ) and choosing certain admissible meromorphic solutions of the bulk equations of motion. The latter provides a natural notion of higher Lax connection for 3-dimensional integrable field theories, including a 2-form component B which can be integrated over Cauchy surfaces to produce conserved charges. As a first application of this approach, we show how to construct a generalization of Ward’s ((2+1))-dimensional integrable chiral model from a suitable choice of data in the 5-dimensional theory.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05170-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679535","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 Semi-classical Limit of Spatially Homogeneous Quantum Boltzmann Equation: Asymptotic Expansion 论空间均质量子玻尔兹曼方程的半经典极限：渐近展开

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-21 DOI: 10.1007/s00220-024-05174-5

Ling-Bing He, Xuguang Lu, Mario Pulvirenti, Yu-Long Zhou

{"title":"On Semi-classical Limit of Spatially Homogeneous Quantum Boltzmann Equation: Asymptotic Expansion","authors":"Ling-Bing He, Xuguang Lu, Mario Pulvirenti, Yu-Long Zhou","doi":"10.1007/s00220-024-05174-5","DOIUrl":"10.1007/s00220-024-05174-5","url":null,"abstract":"<div>We continue our previous work He et al. (Commun Math Phys 386: 143–223, 2021) on the limit of the spatially homogeneous quantum Boltzmann equation as the Planck constant (epsilon ) tends to zero, also known as the semi-classical limit. For general interaction potential, we prove the following: (i). The spatially homogeneous quantum Boltzmann equations are locally well-posed in some weighted Sobolev spaces with quantitative estimates uniformly in (epsilon ). (ii). The semi-classical limit can be further described by the following asymptotic expansion formula: <div><div>$$begin{aligned} f^epsilon (t,v)=f_L(t,v)+O(epsilon ^{vartheta }). end{aligned}$$</div></div>This holds locally in time in Sobolev spaces. Here (f^epsilon ) and (f_L) are solutions to the quantum Boltzmann equation and the Fokker–Planck–Landau equation with the same initial data. The convergent rate (0<vartheta le 1) depends on the integrability of the Fourier transform of the particle interaction potential. Our new ingredients lie in a detailed analysis of the Uehling-Uhlenbeck operator from both angular cutoff and non-cutoff perspectives.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679534","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

T-Duality with H-Flux for 2d (sigma )-Models 2d (sigma )-模型的 T-Duality with H-Flux

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-21 DOI: 10.1007/s00220-024-05168-3

Fei Han, Varghese Mathai

引用次数: 0

Refined Topological Recursion Revisited: Properties and Conjectures 再论精炼拓扑递归：特性与猜想

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-21 DOI: 10.1007/s00220-024-05169-2

Kento Osuga

引用次数: 0

The Boltzmann-Grad Limit of the Lorentz Gas in a Union of Lattices 晶格联盟中洛伦兹气体的玻尔兹曼-梯度极限

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-21 DOI: 10.1007/s00220-024-05173-6

Matthew Palmer, Andreas Strömbergsson

{"title":"The Boltzmann-Grad Limit of the Lorentz Gas in a Union of Lattices","authors":"Matthew Palmer, Andreas Strömbergsson","doi":"10.1007/s00220-024-05173-6","DOIUrl":"10.1007/s00220-024-05173-6","url":null,"abstract":"<div>The Lorentz gas describes an ensemble of noninteracting point particles in an infinite array of spherical scatterers. In the present paper we consider the case when the scatterer configuration ({{mathcal {P}}}) is a fixed union of (translated) lattices in ({mathbb {R}}^d), and prove that in the limit of low scatterer density, the particle dynamics converges to a random flight process. In the special case when the lattices in ({{mathcal {P}}}) are pairwise incommensurable, this settles a conjecture from Marklof and Strömbergsson (J Stat Phys 155:1072–1086, 2014). The proof is carried out by applying a framework developed in recent work by Marklof and Strömbergsson (Mem AMS 294, 2024), and central parts of our proof are the construction of an admissible marking of the point set ({{mathcal {P}}}), and the verification of the uniform spherical equidistribution condition required in Marklof and Strömbergsson (Mem AMS 294, 2024). Regarding the random flight process obtained in the low density limit of the Lorentz gas, we prove that it can be reconstructed from the corresponding limiting flight processes arising from the individual commensurability classes of lattices in ({{mathcal {P}}}). We furthermore prove that the free path lengths of the limit flight process have a distribution with a power law tail, whose exponent depends on the number of commensurability classes in ({{mathcal {P}}}).</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05173-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679537","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

Unravelling the Holomorphic Twist: Central Charges 解读全形扭曲：中心电荷

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-15 DOI: 10.1007/s00220-024-05167-4

Pieter Bomans, Jingxiang Wu

引用次数: 0

Classification of Discrete Weak KAM Solutions on Linearly Repetitive Quasi-Periodic Sets 线性重复准周期集上离散弱 KAM 解的分类

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-15 DOI: 10.1007/s00220-024-05161-w

Eduardo Garibaldi, Samuel Petite, Philippe Thieullen

引用次数: 0