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A Gaussian integral that counts regular graphs 计算规则图形的高斯积分
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-09-05 DOI: 10.1063/5.0208715
Oleg Evnin, Weerawit Horinouchi
{"title":"A Gaussian integral that counts regular graphs","authors":"Oleg Evnin, Weerawit Horinouchi","doi":"10.1063/5.0208715","DOIUrl":"https://doi.org/10.1063/5.0208715","url":null,"abstract":"In a recent article [Kawamoto, J. Phys. Complexity 4, 035005 (2023)], Kawamoto evoked statistical physics methods for the problem of counting graphs with a prescribed degree sequence. This treatment involved truncating a particular Taylor expansion at the first two terms, which resulted in the Bender-Canfield estimate for the graph counts. This is surprisingly successful since the Bender-Canfield formula is asymptotically accurate for large graphs, while the series truncation does not a priori suggest a similar level of accuracy. We upgrade this treatment in three directions. First, we derive an exact formula for counting d-regular graphs in terms of a d-dimensional Gaussian integral. Second, we show how to convert this formula into an integral representation for the generating function of d-regular graph counts. Third, we perform explicit saddle point analysis for large graph sizes and identify the saddle point configurations responsible for graph count estimates. In these saddle point configurations, only two of the integration variables condense to significant values, while the remaining ones approach zero for large graphs. This provides an underlying picture that justifies Kawamoto’s earlier findings.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"242 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A generalization for ultradiscrete limit cycles in a certain type of max-plus dynamical systems 对某类最大加动态系统中超离散极限循环的概括
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-30 DOI: 10.1063/5.0203186
Shousuke Ohmori, Yoshihiro Yamazaki
{"title":"A generalization for ultradiscrete limit cycles in a certain type of max-plus dynamical systems","authors":"Shousuke Ohmori, Yoshihiro Yamazaki","doi":"10.1063/5.0203186","DOIUrl":"https://doi.org/10.1063/5.0203186","url":null,"abstract":"Dynamical properties of a generalized max-plus model for ultradiscrete limit cycles are investigated. This model includes both the negative feedback model and the Sel’kov model. It exhibits the Neimark–Sacker bifurcation, and possesses stable and unstable ultradiscrete limit cycles. The number of discrete states in the limit cycles can be analytically determined and its approximate relation is proposed. Additionally, relationship between the max-plus model and the two-dimensional normal form of the border collision bifurcation is discussed.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"57 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Asymptotic stability to semi-stationary Boussinesq equations without thermal conduction 无热传导半稳态布森斯克方程的渐近稳定性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-30 DOI: 10.1063/5.0150791
Jianguo Li
{"title":"Asymptotic stability to semi-stationary Boussinesq equations without thermal conduction","authors":"Jianguo Li","doi":"10.1063/5.0150791","DOIUrl":"https://doi.org/10.1063/5.0150791","url":null,"abstract":"We study the stability problem of steady solutions to the semi-stationary Boussinesq equations in the strip domain R2×(0,1). For an equilibrium state with any general steady solution θe which satisfies ϑe > m > 0, we show the global existence and asymptotic behavior of solutions to the system with the no-slip boundary condition when the initial temperature is close enough to it. Thus such a steady solution is asymptotically stable, which reflects the well-known phenomenon of Rayleigh-Taylor stability.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"21 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Contact topology and electromagnetism: The Weinstein conjecture and Beltrami-Maxwell fields 接触拓扑学与电磁学：韦恩斯坦猜想和贝尔特拉米-麦克斯韦尔场
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-29 DOI: 10.1063/5.0202751
Shin-itiro Goto
{"title":"Contact topology and electromagnetism: The Weinstein conjecture and Beltrami-Maxwell fields","authors":"Shin-itiro Goto","doi":"10.1063/5.0202751","DOIUrl":"https://doi.org/10.1063/5.0202751","url":null,"abstract":"We draw connections between contact topology and Maxwell fields in vacuo on three-dimensional closed Riemannian submanifolds in four-dimensional Lorentzian manifolds. This is accomplished by showing that contact topological methods can be applied to reveal topological features of a class of solutions to Maxwell’s equations. This class of Maxwell fields is such that electric fields are parallel to magnetic fields. In addition these electromagnetic fields are composed of the so-called Beltrami fields. We employ several theorems resolving the Weinstein conjecture on closed manifolds with contact structures and stable Hamiltonian structures, where this conjecture refers to the existence of periodic orbits of the Reeb vector fields. Here a contact form is a special case of a stable Hamiltonian structure. After showing how to relate Reeb vector fields with electromagnetic 1-forms, we apply a theorem regarding contact manifolds and an improved theorem regarding stable Hamiltonian structures. Then a closed field line is shown to exist, where field lines are generated by Maxwell fields. In addition, electromagnetic energies are shown to be conserved along the Reeb vector fields.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"6 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Spectral analysis of the Dirac operator with a singular interaction on a broken line 断线上具有奇异相互作用的狄拉克算子的谱分析
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-27 DOI: 10.1063/5.0202693
Dale Frymark, Markus Holzmann, Vladimir Lotoreichik
{"title":"Spectral analysis of the Dirac operator with a singular interaction on a broken line","authors":"Dale Frymark, Markus Holzmann, Vladimir Lotoreichik","doi":"10.1063/5.0202693","DOIUrl":"https://doi.org/10.1063/5.0202693","url":null,"abstract":"We consider the one-parametric family of self-adjoint realizations of the two-dimensional massive Dirac operator with a Lorentz scalar δ-shell interaction of strength τ∈R{−2,0,2} supported on a broken line of opening angle 2ω with ω∈(0,π2). The essential spectrum of any such self-adjoint realization is symmetric with respect to the origin with a gap around zero whose size depends on the mass and, for τ < 0, also on the strength of the interaction, but does not depend on ω. As the main result, we prove that for any N∈N and strength τ ∈ (−∞, 0){−2} the discrete spectrum of any such self-adjoint realization has at least N discrete eigenvalues, with multiplicities taken into account, in the gap of the essential spectrum provided that ω is sufficiently small. Moreover, we obtain an explicit estimate on ω sufficient for this property to hold. For τ ∈ (0, ∞){2}, the discrete spectrum consists of at most one simple eigenvalue.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"4 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A Livšic-type theorem and some regularity properties for nonadditive sequences of potentials 李夫希奇型定理和非正交势序列的一些正则特性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-23 DOI: 10.1063/5.0181706
Carllos Eduardo Holanda, Eduardo Santana
{"title":"A Livšic-type theorem and some regularity properties for nonadditive sequences of potentials","authors":"Carllos Eduardo Holanda, Eduardo Santana","doi":"10.1063/5.0181706","DOIUrl":"https://doi.org/10.1063/5.0181706","url":null,"abstract":"We study some notions of cohomology for asymptotically additive sequences and prove a Livšic-type result for almost additive sequences of potentials. As a consequence, we are able to characterize almost additive sequences based on their equilibrium measures and also show how to obtain almost (and asymptotically) additive sequences of Hölder continuous functions satisfying the bounded variation condition (with a unique equilibrium measure) and which are not physically equivalent to any additive sequence generated by a Hölder continuous function. Moreover, we also use our main result to suggest a classification of almost additive sequences based on physical equivalence relations with respect to the classical additive setup.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A quasi-local, functional analytic detection method for stationary limit surfaces of black hole spacetimes 黑洞时空静止极限面的准局部函数解析探测方法
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-23 DOI: 10.1063/5.0207754
Christian Röken
{"title":"A quasi-local, functional analytic detection method for stationary limit surfaces of black hole spacetimes","authors":"Christian Röken","doi":"10.1063/5.0207754","DOIUrl":"https://doi.org/10.1063/5.0207754","url":null,"abstract":"We present a quasi-local, functional analytic method to locate and invariantly characterize the stationary limit surfaces of black hole spacetimes with stationary regions. The method is based on ellipticity-hyperbolicity transitions of the Dirac, Klein–Gordon, Maxwell, and Fierz–Pauli Hamiltonians defined on spacelike hypersurfaces of such black hole spacetimes, which occur only at the locations of stationary limit surfaces and can be ascertained from the behaviors of the principal symbols of the Hamiltonians. Therefore, since it relates solely to the effects that stationary limit surfaces have on the time evolutions of the corresponding elementary fermions and bosons, this method is profoundly different from the usual detection procedures that employ either scalar polynomial curvature invariants or Cartan invariants, which, in contrast, make use of the local geometries of the underlying black hole spacetimes. As an application, we determine the locations of the stationary limit surfaces of the Kerr–Newman, Schwarzschild–de Sitter, and Taub–NUT black hole spacetimes. Finally, we show that for black hole spacetimes with static regions, our functional analytic method serves as a quasi-local event horizon detector and gives rise to a relational concept of black hole entropy.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Nonexistence of closed timelike geodesics in Kerr spacetimes 克尔空间中不存在封闭的时间似大地线
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-23 DOI: 10.1063/5.0221959
Giulio Sanzeni
{"title":"Nonexistence of closed timelike geodesics in Kerr spacetimes","authors":"Giulio Sanzeni","doi":"10.1063/5.0221959","DOIUrl":"https://doi.org/10.1063/5.0221959","url":null,"abstract":"The Kerr-star spacetime is the extension over the horizons and in the negative radial region of the Kerr spacetime. Despite the presence of closed timelike curves below the inner horizon, we prove that the timelike geodesics cannot be closed in the Kerr-star spacetime. Since the existence of closed null geodesics was ruled out by the author in Sanzeni [arXiv:2308.09631v3 (2024)], this result shows the absence of closed causal geodesics in the Kerr-star spacetime.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"72 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Traveling waves for a nonlocal diffusion system with asymmetric kernels and delays 具有非对称内核和延迟的非局部扩散系统的游波
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-23 DOI: 10.1063/5.0184913
Yun-Rui Yang, Lu Yang, Ke-Wang Mu
{"title":"Traveling waves for a nonlocal diffusion system with asymmetric kernels and delays","authors":"Yun-Rui Yang, Lu Yang, Ke-Wang Mu","doi":"10.1063/5.0184913","DOIUrl":"https://doi.org/10.1063/5.0184913","url":null,"abstract":"This paper mainly deals with the (non)existence, asymptotic behaviors and uniqueness of traveling waves to a nonlocal diffusion system with asymmetric kernels and delays for quasi-monotone case. The difference from some previous works is the asymmetry reflected in both diffusion and reaction terms, and this not only has an impact on the positivity of minimal wave speed and the wave profiles of traveling waves with the same speed spreading from the left and right of the x-axis, but also leads to some difficulties for the nonexistence and asymptotic behaviors of traveling waves, which are overcome by using new techniques. Thereby, the results for traveling waves of nonlocal diffusion equations with symmetric kernels and with (or without) delays are improved to equations with asymmetric kernels, and those conclusions for scalar equations and systems with Laplace diffusion and local nonlinearities are also generalized to the nonlocal case. Finally, some concrete applications and numerical simulations are shown to confirm our theoretical results.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 quantum Guerra–Morato action functional 关于量子格拉-莫拉托作用函数
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-08-21 DOI: 10.1063/5.0207422
Josué Knorst, Artur O. Lopes
{"title":"On the quantum Guerra–Morato action functional","authors":"Josué Knorst, Artur O. Lopes","doi":"10.1063/5.0207422","DOIUrl":"https://doi.org/10.1063/5.0207422","url":null,"abstract":"Given a smooth potential W:Tn→R on the torus, the Quantum Guerra–Morato action functional is given by I(ψ)=∫(DvDv*2(x)−W(x))a(x)2dx, where ψ is described by ψ=aeiuℏ, u=v+v*2, a=ev*−v2ℏ, v, v* are real functions, ∫a2(x)dx = 1, and D is the derivative on x ∈ Tn. It is natural to consider the constraint div(a2Du) = 0, which means flux zero. The a and u obtained from a critical solution (under variations τ) for such action functional, fulfilling such constraints, satisfy the Hamilton-Jacobi equation with a quantum potential. Denote ′ =ddτ. We show that the expression for the second variation of a critical solution is given by ∫a2D[v′] D[(v*)′] dx. Introducing the constraint ∫a2Du dx = V, we also consider later an associated dual eigenvalue problem. From this follows a transport and a kind of eikonal equation.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"32 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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