Communications in Mathematical Physics最新文献_第8页

Quantisation via Branes and Minimal Resolution 通过枝蔓和最小分辨率量化

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s00220-024-05137-w

Jian Qiu

引用次数: 0

Diffusive Limit of the Boltzmann Equation in Bounded Domains 有界域中波尔兹曼方程的扩散极限

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s00220-024-05152-x

Zhimeng Ouyang, Lei Wu

{"title":"Diffusive Limit of the Boltzmann Equation in Bounded Domains","authors":"Zhimeng Ouyang, Lei Wu","doi":"10.1007/s00220-024-05152-x","DOIUrl":"10.1007/s00220-024-05152-x","url":null,"abstract":"<div>The investigation of rigorous justification of the hydrodynamic limits in bounded domains has seen significant progress in recent years. While some headway has been made for the diffuse-reflection boundary case (Esposito et al. in Ann PDE 4:1–119, 2018; Ghost effect from Boltzmann theory. arXiv:2301.09427, 2023; Jang and Kim in Ann PDE 7:103, 2021), the more intricate in-flow boundary case, where the leading-order boundary layer effect cannot be neglected, still poses an unresolved challenge. In this study, we tackle the stationary and evolutionary Boltzmann equations, considering the in-flow boundary conditions within both convex and non-convex bounded domains, and demonstrate their diffusive limits in (L^2). Our approach hinges on a groundbreaking insight: a remarkable gain of (varepsilon ^{frac{1}{2}}) in the kernel estimate, which arises from a meticulous selection of test functions and the careful application of conservation laws. Additionally, we introduce a boundary layer with a grazing-set cutoff and investigate its BV regularity estimates to effectively control the source terms in the remainder equation with the help of the Hardy’s inequality.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142595536","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

Decoupling by Local Random Unitaries without Simultaneous Smoothing, and Applications to Multi-user Quantum Information Tasks 无需同时平滑的局部随机单元解耦及其在多用户量子信息任务中的应用

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s00220-024-05156-7

Pau Colomer, Andreas Winter

{"title":"Decoupling by Local Random Unitaries without Simultaneous Smoothing, and Applications to Multi-user Quantum Information Tasks","authors":"Pau Colomer, Andreas Winter","doi":"10.1007/s00220-024-05156-7","DOIUrl":"10.1007/s00220-024-05156-7","url":null,"abstract":"<div>We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old (Dupuis et al. in Commun Math Phys 328:251–284, 2014) and new methods (Dupuis in IEEE Trans Inf Theory 69:7784–7792, 2023), we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of Rényi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, which are additionally optimal for entanglement of assistance and state merging.\u0000</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05156-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142595552","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

Linear Programming with Unitary-Equivariant Constraints 带单变量约束的线性规划

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s00220-024-05108-1

Dmitry Grinko, Maris Ozols

{"title":"Linear Programming with Unitary-Equivariant Constraints","authors":"Dmitry Grinko, Maris Ozols","doi":"10.1007/s00220-024-05108-1","DOIUrl":"10.1007/s00220-024-05108-1","url":null,"abstract":"<div>Unitary equivariance is a natural symmetry that occurs in many contexts in physics and mathematics. Optimization problems with such symmetry can often be formulated as semidefinite programs for a (d^{p+q})-dimensional matrix variable that commutes with (U^{otimes p} otimes {bar{U}}^{otimes q}), for all (U in textrm{U}(d)). Solving such problems naively can be prohibitively expensive even if (p+q) is small but the local dimension d is large. We show that, under additional symmetry assumptions, this problem reduces to a linear program that can be solved in time that does not scale in d, and we provide a general framework to execute this reduction under different types of symmetries. The key ingredient of our method is a compact parametrization of the solution space by linear combinations of walled Brauer algebra diagrams. This parametrization requires the idempotents of a Gelfand–Tsetlin basis, which we obtain by adapting a general method inspired by the Okounkov–Vershik approach. To illustrate potential applications of our framework, we use several examples from quantum information: deciding the principal eigenvalue of a quantum state, quantum majority vote, asymmetric cloning and transformation of a black-box unitary. We also outline a possible route for extending our method to general unitary-equivariant semidefinite programs.\u0000</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05108-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142595537","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

Wilson Lines in the Abelian Lattice Higgs Model 非等边晶格希格斯模型中的威尔逊线

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-05 DOI: 10.1007/s00220-024-05128-x

Malin P. Forsström

{"title":"Wilson Lines in the Abelian Lattice Higgs Model","authors":"Malin P. Forsström","doi":"10.1007/s00220-024-05128-x","DOIUrl":"10.1007/s00220-024-05128-x","url":null,"abstract":"<div>Lattice gauge theories are lattice approximations of the Yang–Mills theory in physics. The abelian lattice Higgs model is one of the simplest examples of a lattice gauge theory interacting with an external field. In a previous paper (Forsström et al. in Math Phys 4(2):257–329, 2023), we calculated the leading order term of the expected value of Wilson loop observables in the low-temperature regime of the abelian lattice Higgs model on ({mathbb {Z}}^4,) with structure group (G = {mathbb {Z}}_n) for some (n ge 2.) In the absence of a Higgs field, these are important observables since they exhibit a phase transition which can be interpreted as distinguishing between regions with and without quark confinement. However, in the presence of a Higgs field, this is no longer the case, and a more relevant family of observables are so-called open Wilson lines. In this paper, we extend and refine the ideas introduced in Forsström et al. (Math Phys 4(2):257–329, 2023) to calculate the leading order term of the expected value of the more general Wilson line observables. Using our main result, we then calculate the leading order term of several natural ratios of expected values and confirm the behavior predicted by physicists.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05128-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587712","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

A Proof of a Conjecture of Gukov–Pei–Putrov–Vafa 古科夫-裴-普特罗夫-瓦法猜想的证明

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-05 DOI: 10.1007/s00220-024-05136-x

Yuya Murakami

引用次数: 0

Onsager Theory of Turbulence, the Josephson–Anderson Relation, and the D’Alembert Paradox 湍流的昂萨格理论、约瑟夫森-安德森关系和达朗贝尔悖论

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-11-05 DOI: 10.1007/s00220-024-05126-z

Hao Quan, Gregory L. Eyink

{"title":"Onsager Theory of Turbulence, the Josephson–Anderson Relation, and the D’Alembert Paradox","authors":"Hao Quan, Gregory L. Eyink","doi":"10.1007/s00220-024-05126-z","DOIUrl":"10.1007/s00220-024-05126-z","url":null,"abstract":"<div>The Josephson–Anderson relation, valid for the incompressible Navier–Stokes solutions which describe flow around a solid body, equates the power dissipated by drag instantaneously to the flux of vorticity across the flow lines of the potential Euler solution considered by d’Alembert. Its derivation involves a decomposition of the velocity field into this background potential-flow field and a solenoidal field corresponding to the rotational wake behind the body, with the flux term describing a transfer from the interaction energy between the two fields and into kinetic energy of the rotational flow. We establish the validity of the Josephson–Anderson relation for the weak solutions of the Euler equations obtained in the zero-viscosity limit, with one transfer term due to inviscid vorticity flux and the other due to a viscous skin-friction anomaly. Furthermore, we establish weak forms of the local balance equations for both interaction and rotational energies. We define nonlinear spatial fluxes of these energies and show that the asymptotic flux of interaction energy to the wall equals the anomalous skin-friction term in the Josephson–Anderson relation. However, when the Euler solution satisfies a condition of vanishing normal velocity at the wall, then the anomalous term vanishes. In this case, we can show also that the asymptotic flux of rotational energy to the wall must vanish and we obtain in the rotational wake the Onsager–Duchon–Robert relation between viscous dissipation anomaly and inertial dissipation due to scale-cascade. In this way we establish a precise connection between the Josephson–Anderson relation and the Onsager theory of turbulence, and we provide a novel resolution of the d’Alembert paradox.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587821","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 the Limit Problem Arising in the Kinetic Derivation of a Cahn–Hilliard Equation 关于卡恩-希利亚德方程动力学推导中出现的极限问题

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1007/s00220-024-05142-z

Charles Elbar, Benoît Perthame, Jakub Skrzeczkowski

引用次数: 0

(alpha )-z-Rényi Divergences in von Neumann Algebras: Data Processing Inequality, Reversibility, and Monotonicity Properties in (alpha ,z) von Neumann Algebras 中的（alpha ）-z-Rényi 分歧：（alpha ,z）中的数据处理不等式、可逆性和单调性特性

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1007/s00220-024-05124-1

Fumio Hiai, Anna Jenčová

{"title":"(alpha )-z-Rényi Divergences in von Neumann Algebras: Data Processing Inequality, Reversibility, and Monotonicity Properties in (alpha ,z)","authors":"Fumio Hiai, Anna Jenčová","doi":"10.1007/s00220-024-05124-1","DOIUrl":"10.1007/s00220-024-05124-1","url":null,"abstract":"<div>We study the (alpha )-z-Rényi divergences (D_{alpha ,z}(psi Vert varphi )) where (alpha ,z>0) ((alpha ne 1)) for normal positive functionals (psi ,varphi ) on general von Neumann algebras, introduced in Kato and Ueda (arXiv:2307.01790) and Kato (arXiv:2311.01748). We prove the variational expressions and the data processing inequality (DPI) for the (alpha )-z-Rényi divergences. We establish the sufficiency theorem for (D_{alpha ,z}(psi Vert varphi )), saying that for ((alpha ,z)) inside the DPI bounds, the equality (D_{alpha ,z}(psi circ gamma Vert varphi circ gamma )=D_{alpha ,z}(psi Vert varphi )<infty ) in the DPI under a quantum channel (or a normal 2-positive unital map) (gamma ) implies the reversibility of (gamma ) with respect to (psi ,varphi ). Moreover, we show the monotonicity properties of (D_{alpha ,z}(psi Vert varphi )) in the parameters (alpha ,z) and their limits to the normalized relative entropy as (alpha nearrow 1) and (alpha searrow 1).</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 11","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05124-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518890","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

Invariant KAM Tori Around Annular Vortex Patches for 2D Euler Equations 二维欧拉方程环形涡斑周围的不变 KAM Tori

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2024-10-24 DOI: 10.1007/s00220-024-05141-0

Zineb Hassainia, Taoufik Hmidi, Emeric Roulley

引用次数: 0