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Logarithmic singularity in the density four-point function of two-dimensional critical percolation in the bulk 体中二维临界渗流密度四点函数的对数奇异性
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-27 DOI: arxiv-2403.18576
Federico Camia, Yu Feng
{"title":"Logarithmic singularity in the density four-point function of two-dimensional critical percolation in the bulk","authors":"Federico Camia, Yu Feng","doi":"arxiv-2403.18576","DOIUrl":"https://doi.org/arxiv-2403.18576","url":null,"abstract":"We provide definitive proof of the logarithmic nature of the percolation\u0000conformal field theory in the bulk by showing that the four-point function of\u0000the density operator has a logarithmic divergence as two points collide and\u0000that the same divergence appears in the operator product expansion (OPE) of two\u0000density operators. The right hand side of the OPE contains two operators with\u0000the same scaling dimension, one of them multiplied by a term with a logarithmic\u0000singularity. Our method involves a probabilistic analysis of the percolation\u0000events contributing to the four-point function. It does not require algebraic\u0000considerations, nor taking the $Q to 1$ limit of the $Q$-state Potts model,\u0000and is amenable to a rigorous mathematical formulation. The logarithmic\u0000divergence appears as a consequence of scale invariance combined with\u0000independence.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Universality classes for percolation models with long-range correlations 具有长程相关性的渗流模型的普遍性类别
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-27 DOI: arxiv-2403.18787
Christopher Chalhoub, Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
{"title":"Universality classes for percolation models with long-range correlations","authors":"Christopher Chalhoub, Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez","doi":"arxiv-2403.18787","DOIUrl":"https://doi.org/arxiv-2403.18787","url":null,"abstract":"We consider a class of percolation models where the local occupation\u0000variables have long-range correlations decaying as a power law $sim r^{-a}$ at\u0000large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial\u0000dimension. For several of these models, we present both, rigorous analytical\u0000results and matching simulations that determine the critical exponents\u0000characterizing the fixed point associated to their phase transition, which is\u0000of second order. The exact values we obtain are rational functions of the two\u0000parameters $a$ and $d$ alone, and do not depend on the specifics of the model.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On AdS$_4$ deformations of celestial symmetries 关于天体对称的 AdS$_4$ 变形
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-26 DOI: arxiv-2403.18011
Roland Bittleston, Giuseppe Bogna, Simon Heuveline, Adam Kmec, Lionel Mason, David Skinner
{"title":"On AdS$_4$ deformations of celestial symmetries","authors":"Roland Bittleston, Giuseppe Bogna, Simon Heuveline, Adam Kmec, Lionel Mason, David Skinner","doi":"arxiv-2403.18011","DOIUrl":"https://doi.org/arxiv-2403.18011","url":null,"abstract":"Celestial holography has led to the discovery of new symmetry algebras\u0000arising from the study of collinear limits of perturbative gravity amplitudes\u0000in flat space. We explain from the twistor perspective how a non-vanishing\u0000cosmological constant $Lambda$ naturally modifies the celestial chiral\u0000algebra. The cosmological constant deforms the Poisson bracket on twistor\u0000space, so the corresponding deformed algebra of Hamiltonians under the new\u0000bracket is automatically consistent. This algebra is equivalent to that\u0000recently found by Taylor and Zhu. We find a number of variations of the\u0000deformed algebra. We give the Noether charges arising from the expression of\u0000this algebra as a symmetry of the twistor action for self-dual gravity with\u0000cosmological constant.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum fields on projective geometries 投影几何上的量子场
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-26 DOI: arxiv-2403.17996
Daniel Spitz
{"title":"Quantum fields on projective geometries","authors":"Daniel Spitz","doi":"arxiv-2403.17996","DOIUrl":"https://doi.org/arxiv-2403.17996","url":null,"abstract":"Considering homogeneous four-dimensional space-time geometries within real\u0000projective geometry provides a mathematically well-defined framework to discuss\u0000their deformations and limits without the appearance of coordinate\u0000singularities. On Lie algebra level the related conjugacy limits act\u0000isomorphically to concatenations of contractions. We axiomatically introduce\u0000projective quantum fields on homogeneous space-time geometries, based on\u0000correspondingly generalized unitary transformation behavior and\u0000projectivization of the field operators. Projective correlators and their\u0000expectation values remain well-defined in all geometry limits, which includes\u0000their ultraviolet and infrared limits. They can degenerate with support on\u0000space-time boundaries and other lower-dimensional space-time subspaces. We\u0000explore fermionic and bosonic superselection sectors as well as the\u0000irreducibility of projective quantum fields. Dirac fermions appear, which obey\u0000spin-statistics as composite quantum fields. The framework might be of use for\u0000the consistent description of quantum fields in holographic correspondences and\u0000their flat limits.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extremality of stabilizer states 稳定器状态的极端性
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-20 DOI: arxiv-2403.13632
Kaifeng Bu
{"title":"Extremality of stabilizer states","authors":"Kaifeng Bu","doi":"arxiv-2403.13632","DOIUrl":"https://doi.org/arxiv-2403.13632","url":null,"abstract":"We investigate the extremality of stabilizer states to reveal their\u0000exceptional role in the space of all $n$-qubit/qudit states. We establish\u0000uncertainty principles for the characteristic function and the Wigner function\u0000of states, respectively. We find that only stabilizer states achieve saturation\u0000in these principles. Furthermore, we prove a general theorem that stabilizer\u0000states are extremal for convex information measures invariant under local\u0000unitaries. We explore this extremality in the context of various quantum\u0000information and correlation measures, including entanglement entropy,\u0000conditional entropy and other entanglement measures. Additionally, leveraging\u0000the recent discovery that stabilizer states are the limit states under quantum\u0000convolution, we establish the monotonicity of the entanglement entropy and\u0000conditional entropy under quantum convolution. These results highlight the\u0000remarkable information-theoretic properties of stabilizer states. Their\u0000extremality provides valuable insights into their ability to capture\u0000information content and correlations, paving the way for further exploration of\u0000their potential in quantum information processing.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140197803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces 非简单连接流形上的 Floquet-Bloch 函数、Aharonov-Bohm 通量和浸没曲面的保角不变式
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-17 DOI: arxiv-2403.11161
I. A. Taimanov
{"title":"Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces","authors":"I. A. Taimanov","doi":"arxiv-2403.11161","DOIUrl":"https://doi.org/arxiv-2403.11161","url":null,"abstract":"Spectral (Bloch) varieties of multidimensional differential operators on\u0000non-simply connected manifolds are defined. In their terms it is given a\u0000description of the analytical dependence of the spectra of magnetic Laplacians\u0000on non-simply connected manifolds on the values of the Aharonov-Bohm fluxes and\u0000a construction of analogues of spectral curves for two-dimensional Dirac\u0000operators on Riemann surfaces and, thereby, new conformal invariants of\u0000immersions of surfaces into 3- and 4-dimensional Euclidean spaces.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discrete Dynamics on Locally Conformal Framework 局部共形框架上的离散动力学
arXiv - PHYS - Mathematical Physics Pub Date : 2024-03-01 DOI: arxiv-2403.00312
Oğul Esen, Ayten Gezici, Hasan Gümral
{"title":"Discrete Dynamics on Locally Conformal Framework","authors":"Oğul Esen, Ayten Gezici, Hasan Gümral","doi":"arxiv-2403.00312","DOIUrl":"https://doi.org/arxiv-2403.00312","url":null,"abstract":"In this paper, we address the globalization problem of discrete Lagrangian\u0000and Hamiltonian dynamics in locally conformal framework.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symmetries and exact solutions of the diffusive Holling-Tanner prey-predator model 扩散霍林-坦纳猎物-捕食者模型的对称性和精确解
arXiv - PHYS - Mathematical Physics Pub Date : 2024-02-29 DOI: arxiv-2402.19098
Roman Cherniha, Vasyl' Davydovych
{"title":"Symmetries and exact solutions of the diffusive Holling-Tanner prey-predator model","authors":"Roman Cherniha, Vasyl' Davydovych","doi":"arxiv-2402.19098","DOIUrl":"https://doi.org/arxiv-2402.19098","url":null,"abstract":"We consider the classical Holling-Tanner model extended on 1D space by\u0000introducing the diffusion term. Making a reasonable simplification, the\u0000diffusive Holling-Tanner system is studied by means of symmetry based methods.\u0000Lie and Q-conditional (nonclassical) symmetries are identified. The symmetries\u0000obtained are applied for finding a wide range of exact solutions, their\u0000properties are studied and a possible biological interpretation is proposed. 3D\u0000plots of the most interesting solutions are drown as well.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_{m})$ gravity 虫洞的暗能量和暗物质构型以及非度量利玛窦流和 $F(R,T,Q,T_{m})$ 引力的溶解性层次结构
arXiv - PHYS - Mathematical Physics Pub Date : 2024-02-29 DOI: arxiv-2402.19362
Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva
{"title":"Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and $F(R,T,Q,T_{m})$ gravity","authors":"Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva","doi":"arxiv-2402.19362","DOIUrl":"https://doi.org/arxiv-2402.19362","url":null,"abstract":"We extend the anholonomic frame and connection deformation method, AFCDM, for\u0000constructing exact and parametric solutions in general relativity, GR, to\u0000geometric flow models and modified gravity theories, MGTs, with nontrivial\u0000torsion and nonmetricity fields. Following abstract geometric or variational\u0000methods, we can derive corresponding systems of nonmetric gravitational and\u0000matter field equations which consist of very sophisticated systems of coupled\u0000nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and\u0000applying the AFCDM, we prove that such systems of PDEs can be decoupled and\u0000integrated in general forms for generic off-diagonal metric structures and\u0000generalized affine connections. We generate new classes of quasi-stationary\u0000solutions (which do not depend on time like coordinates) and study the physical\u0000properties of some physically important examples. Such exact or parametric\u0000solutions are determined by nonmetric solitonic distributions and/or\u0000ellipsoidal deformations of wormhole hole configurations. It is not possible to\u0000describe the thermodynamic properties of such solutions in the framework of the\u0000Bekenstein-Hawking paradigm because such metrics do not involve, in general,\u0000certain horizons, duality, or holographic configurations. Nevertheless, we can\u0000always elaborate on associated Grigori Perelman thermodynamic models elaborated\u0000for nonmetric geometric flows. In explicit form, applying the AFCDM, we\u0000construct and study the physical implications of new classes of traversable\u0000wormhole solutions describing solitonic deformation and dissipation of\u0000non-Riemannian geometric objects. Such models with nontrivial gravitational\u0000off-diagonal vacuum are important for elaborating models of dark energy and\u0000dark matter involving wormhole configurations and solitonic-type structure\u0000formation.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new interacting Fock space, the Quon algebra with operator parameter and its Wick's theorem 一种新的相互作用的福克空间、带算子参数的昆代数及其威克定理
arXiv - PHYS - Mathematical Physics Pub Date : 2024-02-29 DOI: arxiv-2402.18961
Yungang Lu
{"title":"A new interacting Fock space, the Quon algebra with operator parameter and its Wick's theorem","authors":"Yungang Lu","doi":"arxiv-2402.18961","DOIUrl":"https://doi.org/arxiv-2402.18961","url":null,"abstract":"Motivated by the creation-annihilation operators in a newly defined\u0000interacting Fock space, we initiate the introduction and the study of the Quon\u0000algebra. This algebra serves as an extension of the conventional quon algebra,\u0000where the traditional constant parameter $q$ found in the $q$--commutation\u0000relation is replaced by a specific operator. Importantly, our investigation\u0000aims to establish Wick's theorem in the Quon algebra, offering valuable\u0000insights into its properties and applications.","PeriodicalId":501275,"journal":{"name":"arXiv - PHYS - Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140001313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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