We provide definitive proof of the logarithmic nature of the percolation conformal field theory in the bulk by showing that the four-point function of the density operator has a logarithmic divergence as two points collide and that the same divergence appears in the operator product expansion (OPE) of two density operators. The right hand side of the OPE contains two operators with the same scaling dimension, one of them multiplied by a term with a logarithmic singularity. Our method involves a probabilistic analysis of the percolation events contributing to the four-point function. It does not require algebraic considerations, nor taking the $Q to 1$ limit of the $Q$-state Potts model, and is amenable to a rigorous mathematical formulation. The logarithmic divergence appears as a consequence of scale invariance combined with independence.
通过证明密度算子的四点函数在两点碰撞时具有对数发散性，以及同样的发散性出现在两个密度算子的算子乘积展开（OPE）中，我们提供了体中渗滤共形场论对数性质的确证。OPE 的右侧包含两个具有相同缩放维度的算子，其中一个乘以一个具有对数奇异性的项。我们的方法涉及对促成四点函数的渗流事件的概率分析。它不需要代数学的考虑，也不需要对$Q$态波茨模型的$Q to 1$ 极限进行计算，而且可以用严格的数学公式来表述。对数背离的出现是尺度不变性与独立性相结合的结果。
{"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}
Christopher Chalhoub, Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For several of these models, we present both, rigorous analytical results and matching simulations that determine the critical exponents characterizing the fixed point associated to their phase transition, which is of second order. The exact values we obtain are rational functions of the two parameters $a$ and $d$ alone, and do not depend on the specifics of the model.
{"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}
Roland Bittleston, Giuseppe Bogna, Simon Heuveline, Adam Kmec, Lionel Mason, David Skinner
Celestial holography has led to the discovery of new symmetry algebras arising from the study of collinear limits of perturbative gravity amplitudes in flat space. We explain from the twistor perspective how a non-vanishing cosmological constant $Lambda$ naturally modifies the celestial chiral algebra. The cosmological constant deforms the Poisson bracket on twistor space, so the corresponding deformed algebra of Hamiltonians under the new bracket is automatically consistent. This algebra is equivalent to that recently found by Taylor and Zhu. We find a number of variations of the deformed algebra. We give the Noether charges arising from the expression of this algebra as a symmetry of the twistor action for self-dual gravity with cosmological constant.
{"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}
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On Lie algebra level the related conjugacy limits act isomorphically to concatenations of contractions. We axiomatically introduce projective quantum fields on homogeneous space-time geometries, based on correspondingly generalized unitary transformation behavior and projectivization of the field operators. Projective correlators and their expectation values remain well-defined in all geometry limits, which includes their ultraviolet and infrared limits. They can degenerate with support on space-time boundaries and other lower-dimensional space-time subspaces. We explore fermionic and bosonic superselection sectors as well as the irreducibility of projective quantum fields. Dirac fermions appear, which obey spin-statistics as composite quantum fields. The framework might be of use for the consistent description of quantum fields in holographic correspondences and their flat limits.
{"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}
We investigate the extremality of stabilizer states to reveal their exceptional role in the space of all $n$-qubit/qudit states. We establish uncertainty principles for the characteristic function and the Wigner function of states, respectively. We find that only stabilizer states achieve saturation in these principles. Furthermore, we prove a general theorem that stabilizer states are extremal for convex information measures invariant under local unitaries. We explore this extremality in the context of various quantum information and correlation measures, including entanglement entropy, conditional entropy and other entanglement measures. Additionally, leveraging the recent discovery that stabilizer states are the limit states under quantum convolution, we establish the monotonicity of the entanglement entropy and conditional entropy under quantum convolution. These results highlight the remarkable information-theoretic properties of stabilizer states. Their extremality provides valuable insights into their ability to capture information content and correlations, paving the way for further exploration of their potential in quantum information processing.
{"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}
Spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds are defined. In their terms it is given a description of the analytical dependence of the spectra of magnetic Laplacians on non-simply connected manifolds on the values of the Aharonov-Bohm fluxes and a construction of analogues of spectral curves for two-dimensional Dirac operators on Riemann surfaces and, thereby, new conformal invariants of immersions of surfaces into 3- and 4-dimensional Euclidean spaces.
{"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}
In this paper, we address the globalization problem of discrete Lagrangian and Hamiltonian dynamics in locally conformal framework.
在本文中，我们讨论了局部保角框架下离散拉格朗日和哈密顿动力学的全球化问题。
{"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}
We consider the classical Holling-Tanner model extended on 1D space by introducing the diffusion term. Making a reasonable simplification, the diffusive Holling-Tanner system is studied by means of symmetry based methods. Lie and Q-conditional (nonclassical) symmetries are identified. The symmetries obtained are applied for finding a wide range of exact solutions, their properties are studied and a possible biological interpretation is proposed. 3D plots of the most interesting solutions are drown as well.
{"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}
Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev, Assel Zhamysheva
We extend the anholonomic frame and connection deformation method, AFCDM, for constructing exact and parametric solutions in general relativity, GR, to geometric flow models and modified gravity theories, MGTs, with nontrivial torsion and nonmetricity fields. Following abstract geometric or variational methods, we can derive corresponding systems of nonmetric gravitational and matter field equations which consist of very sophisticated systems of coupled nonlinear PDEs. Using nonholonomic frames with dyadic spacetime splitting and applying the AFCDM, we prove that such systems of PDEs can be decoupled and integrated in general forms for generic off-diagonal metric structures and generalized affine connections. We generate new classes of quasi-stationary solutions (which do not depend on time like coordinates) and study the physical properties of some physically important examples. Such exact or parametric solutions are determined by nonmetric solitonic distributions and/or ellipsoidal deformations of wormhole hole configurations. It is not possible to describe the thermodynamic properties of such solutions in the framework of the Bekenstein-Hawking paradigm because such metrics do not involve, in general, certain horizons, duality, or holographic configurations. Nevertheless, we can always elaborate on associated Grigori Perelman thermodynamic models elaborated for nonmetric geometric flows. In explicit form, applying the AFCDM, we construct and study the physical implications of new classes of traversable wormhole solutions describing solitonic deformation and dissipation of non-Riemannian geometric objects. Such models with nontrivial gravitational off-diagonal vacuum are important for elaborating models of dark energy and dark matter involving wormhole configurations and solitonic-type structure formation.
{"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}
Motivated by the creation-annihilation operators in a newly defined interacting Fock space, we initiate the introduction and the study of the Quon algebra. This algebra serves as an extension of the conventional quon algebra, where the traditional constant parameter $q$ found in the $q$--commutation relation is replaced by a specific operator. Importantly, our investigation aims to establish Wick's theorem in the Quon algebra, offering valuable insights into its properties and applications.
{"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}
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