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$SU(1,1)times SU(2)$ approach and the Mandel parameter to the Hamiltonian of two oscillators with weak coupling 具有弱耦合的两个振子的哈密顿的 $SU(1,1)/times SU(2)$ 方法和曼德尔参数
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.08179
J. C. Vega, D. Ojeda-Guillén, R. D. Mota
{"title":"$SU(1,1)times SU(2)$ approach and the Mandel parameter to the Hamiltonian of two oscillators with weak coupling","authors":"J. C. Vega, D. Ojeda-Guillén, R. D. Mota","doi":"arxiv-2409.08179","DOIUrl":"https://doi.org/arxiv-2409.08179","url":null,"abstract":"We study the Hamiltonian of two isotropic oscillators with weak coupling from\u0000an algebraic approach. We write the Hamiltonian of this problem in terms of the\u0000boson generators of the $SU(1,1)$ and $SU(2)$ groups. This allows us to apply\u0000two tilting transformations based on both group similarity transformations to\u0000obtain its energy spectrum and eigenfunctions. Then, we obtain the Mandel\u0000$Q-$parameter of the photon numbers $n_a$ and $n_b$. It is important to note\u0000that in our procedure we consider the case of weak coupling.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"142 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216332","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 realizations of the complex Lie groups $ (F_{4,R})^C, (E_{6,R})^C, (E_{7,R})^C ,(E_{8,R})^C$ and those compact real forms $F_{4,R},E_{6,R},E_{7,R},E_{8,R}$ 关于复数李群 $ (F_{4,R})^C, (E_{6,R})^C, (E_{7,R})^C ,(E_{8,R})^C$ 和那些紧凑实数形式 $F_{4,R},E_{6,R},E_{7,R},E_{8,R}$ 的实数化
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.07760
Toshikazu Miyashita
{"title":"On realizations of the complex Lie groups $ (F_{4,R})^C, (E_{6,R})^C, (E_{7,R})^C ,(E_{8,R})^C$ and those compact real forms $F_{4,R},E_{6,R},E_{7,R},E_{8,R}$","authors":"Toshikazu Miyashita","doi":"arxiv-2409.07760","DOIUrl":"https://doi.org/arxiv-2409.07760","url":null,"abstract":"In order to define the complex exceptional Lie groups $ {F_4}^C, {E_6}^C,\u0000{E_7}^C, {E_8}^C $ and these compact real forms $ F_4,E_6,E_7,E_8 $, we usually\u0000use the Cayley algebra $ mathfrak{C} $. In the present article, we consider\u0000replacing the Cayley algebra $ mathfrak{C} $ with the field of real numbers\u0000$mathbb R$ in the definition of the groups above, and these groups are denoted\u0000as in title above. Our aim is to determine the structure of these groups. We\u0000call realization to determine the structure of the groups.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"283 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216327","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 the space of $2d$ integrable models 关于 2d$ 可积分模型空间
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.08266
Lukas W. Lindwasser
{"title":"On the space of $2d$ integrable models","authors":"Lukas W. Lindwasser","doi":"arxiv-2409.08266","DOIUrl":"https://doi.org/arxiv-2409.08266","url":null,"abstract":"We study infinite dimensional Lie algebras, whose infinite dimensional\u0000mutually commuting subalgebras correspond with the symmetry algebra of $2d$\u0000integrable models. These Lie algebras are defined by the set of infinitesimal,\u0000nonlinear, and higher derivative symmetry transformations present in theories\u0000with a left(right)-moving or (anti)-holomorphic current. We study a large class\u0000of such Lagrangian theories. We classify the commuting subalgebras of the $2d$\u0000free massless scalar, and find the symmetries of the known integrable models\u0000such as sine-Gordon, Liouville, Bullough-Dodd, and Korteweg-de Vries. Along the\u0000way, we find several new sequences of commuting charges, which we conjecture\u0000are charges of integrable models which are new deformations of a single scalar.\u0000After quantizing, the Lie algebra is deformed, and so are their commuting\u0000subalgebras.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216325","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
Practical Introduction to Action-Dependent Field Theories 行动依赖场理论实用导论
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.08340
Manuel de León, Jordi Gaset Rifà, Miguel C. Muñoz-Lecanda, Xavier Rivas, Narciso Román-Roy
{"title":"Practical Introduction to Action-Dependent Field Theories","authors":"Manuel de León, Jordi Gaset Rifà, Miguel C. Muñoz-Lecanda, Xavier Rivas, Narciso Román-Roy","doi":"arxiv-2409.08340","DOIUrl":"https://doi.org/arxiv-2409.08340","url":null,"abstract":"Action-dependent field theories are systems where the Lagrangian or\u0000Hamiltonian depends on new variables that encode the action. After a friendly\u0000introduction, we make a quick presentation of a new mathematical framework for\u0000action-dependent field theory: multicontact geometry. The formalism is\u0000illustrated in a variety of action-dependent Lagrangians, some of which are\u0000regular and other singular, that come from some well-known theories whose\u0000Lagrangians have been modified to incorporate action-dependent terms. Detailed\u0000computations are provided, including the constraint algorithm, in both the\u0000Lagrangian and Hamiltonian formalisms. They include the Klein-Gordon equation,\u0000the Bosonic string theory, Metric-affine gravity, Maxwell's electromagnetism,\u0000(2+1)-dimensional gravity and Chern-Simons equation, and the heat equation and\u0000Burgers' equation.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260526","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
Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution 费米子高斯测试与卷积非高斯测量
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.08180
Nicholas Lyu, Kaifeng Bu
{"title":"Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution","authors":"Nicholas Lyu, Kaifeng Bu","doi":"arxiv-2409.08180","DOIUrl":"https://doi.org/arxiv-2409.08180","url":null,"abstract":"We explore the properties of fermionic convolution defined by fermionic\u0000Gaussian unitary. A key finding is the purity invariance of pure Gaussian\u0000states under this convolution. Leveraging this property, we propose an\u0000efficient protocol to test the fermionic Gaussianity of pure states by using 3\u0000copies of the input states. Furthermore, we introduce a new family of measures\u0000called ``Non-Gaussian Entropy,'' designed to quantify the fermionic\u0000non-Gaussianity of states.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216502","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
Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity 纽曼-彭罗斯形式主义与共形韦尔引力的精确真空解
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.08344
Petr Jizba, Kamil Mudruňka
{"title":"Newman-Penrose formalism and exact vacuum solutions to conformal Weyl gravity","authors":"Petr Jizba, Kamil Mudruňka","doi":"arxiv-2409.08344","DOIUrl":"https://doi.org/arxiv-2409.08344","url":null,"abstract":"We study the exterior solution for a static, spherically symmetric source in\u0000Weyl conformal gravity in terms of the Newman--Penrose formalism. We first show\u0000that both the static, uncharged black hole solution of Mannheim and Kazanas and\u0000the static, charged Reissner--Nordstr\"{o}m-like solution can be found more\u0000easily in this formalism than in the traditional coordinate-basis approach,\u0000where the metric tensor components are taken as the basic variables. Second, we\u0000show that the Newman-Penrose formalism offers a particularly convenient\u0000framework that is well suited for the discussion of conformal gravity solutions\u0000corresponding to Petrov ''type-D'' spacetimes. This is illustrated with a\u0000two-parameter class of wormhole solutions that includes the Ellis--Bronnikov\u0000wormhole solution of Einstein's gravity as a limiting case. Other salient\u0000issues, such as the gauge equivalence of solutions and the inclusion of the\u0000electromagnetic field are also discussed.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260525","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
Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach 延迟常微分方程：从拉格朗日方法到哈密顿方法
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-12 DOI: arxiv-2409.08165
Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko
{"title":"Delay ordinary differential equations: from Lagrangian approach to Hamiltonian approach","authors":"Vladimir Dorodnitsyn, Roman Kozlov, Sergey Meleshko","doi":"arxiv-2409.08165","DOIUrl":"https://doi.org/arxiv-2409.08165","url":null,"abstract":"The paper suggests a Hamiltonian formulation for delay ordinary differential\u0000equations (DODEs). Such equations are related to DODEs with a Lagrangian\u0000formulation via a delay analog of the Legendre transformation. The Hamiltonian\u0000delay operator identity is established. It states the relationship for the\u0000invariance of a delay Hamiltonian functional, appropriate delay variational\u0000equations, and their conserved quantities. The identity is used to formulate a\u0000Noether-type theorem, which provides first integrals for Hamiltonian DODEs with\u0000symmetries. The relationship between the invariance of the delay Hamiltonian\u0000functional and the invariance of the delay variational equations is also\u0000examined. Several examples illustrate the theoretical results.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216321","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 Reference Frames on Homogeneous Spaces 均质空间上的量子参照系
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07231
Jan Głowacki
{"title":"Quantum Reference Frames on Homogeneous Spaces","authors":"Jan Głowacki","doi":"arxiv-2409.07231","DOIUrl":"https://doi.org/arxiv-2409.07231","url":null,"abstract":"This paper initiates a systematic study of operators arising as integrals of\u0000operator-valued functions with respect to positive operator-valued measures and\u0000utilizes these tools to provide relativization maps (Yen) for quantum reference\u0000frames (QRFs) defined on general homogeneous spaces. Properties of\u0000operator-valued integration are first studied and then employed to define\u0000general relativization maps and show their properties. The relativization maps\u0000presented here are defined for QRFs (systems of covariance) based on arbitrary\u0000homogeneous spaces of locally compact second countable topological groups and\u0000are shown to be contracting quantum channels, injective for localizable (norm-1\u0000property) frames and multiplicative for the sharp ones (PVMs), extending the\u0000existing results.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216331","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
The Penrose inequality in spherical symmetry with charge and in Gauss-Bonnet gravity 带电荷的球面对称和高斯-波奈引力中的彭罗斯不等式
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07639
Hari K. Kunduri, Juan Margalef-Bentabol, Sarah Muth
{"title":"The Penrose inequality in spherical symmetry with charge and in Gauss-Bonnet gravity","authors":"Hari K. Kunduri, Juan Margalef-Bentabol, Sarah Muth","doi":"arxiv-2409.07639","DOIUrl":"https://doi.org/arxiv-2409.07639","url":null,"abstract":"We establish the spacetime Penrose inequality in spherical symmetry in\u0000spacetime dimensions $n+1geq3$ with charge and cosmological constant from the\u0000initial data perspective. We also show that this result extends to the\u0000Gauss-Bonnet theory of gravity.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216330","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
Implementation of thermal conduction energy transfer models in the Bifrost Solar atmosphere MHD code 在 Bifrost 太阳大气 MHD 代码中实施热传导能量传递模型
arXiv - MATH - Mathematical Physics Pub Date : 2024-09-11 DOI: arxiv-2409.07074
George Cherry, Boris Gudiksen, Mikolaj Szydlarski
{"title":"Implementation of thermal conduction energy transfer models in the Bifrost Solar atmosphere MHD code","authors":"George Cherry, Boris Gudiksen, Mikolaj Szydlarski","doi":"arxiv-2409.07074","DOIUrl":"https://doi.org/arxiv-2409.07074","url":null,"abstract":"Context: Thermal conductivity provides important contributions to the energy\u0000evolution of the upper solar atmosphere, behaving as a non-linear\u0000concentration-dependent diffusion equation. Recently, different methods have\u0000been offered as best-fit solutions to these problems in specific situations,\u0000but their effectiveness and limitations are rarely discussed. Aims. We\u0000rigorously test the different implementations of solving the conductivity flux,\u0000in the massively-parallel magnetohydrodynamics code, Bifrost, with the aim of\u0000specifying the best scenarios for the use of each method. Methods: We compare\u0000the differences and limitations of explicit versus implicit methods, and\u0000analyse the convergence of a hyperbolic approximation. Among the tests, we use\u0000a newly derived 1st-order self-similar approximation to compare the efficacy of\u0000each method analytically in a 1D pure-thermal test scenario. Results: We find\u0000that although the hyperbolic approximation proves the most accurate and the\u0000fastest to compute in long-running simulations, there is no optimal method to\u0000calculate the mid-term conductivity with both accuracy and efficiency. We also\u0000find that the solution of this approximation is sensitive to the initial\u0000conditions, and can lead to faster convergence if used correctly.\u0000Hyper-diffusivity is particularly useful in aiding the methods to perform\u0000optimally. Conclusions: We discuss recommendations for the use of each method\u0000within more complex simulations, whilst acknowledging the areas of opportunity\u0000for new methods to be developed.","PeriodicalId":501312,"journal":{"name":"arXiv - MATH - Mathematical Physics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216361","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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