Journal of Mathematical Physics Analysis Geometry最新文献

On the polynomial integrability of the critical systems for optimal eigenvalue gaps 最优特征值间隙临界系统的多项式可积性

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-09-01 DOI: 10.1063/5.0140966

Yuzhou Tian, Qiaoling Wei, Meirong Zhang

{"title":"On the polynomial integrability of the critical systems for optimal eigenvalue gaps","authors":"Yuzhou Tian, Qiaoling Wei, Meirong Zhang","doi":"10.1063/5.0140966","DOIUrl":"https://doi.org/10.1063/5.0140966","url":null,"abstract":"This exploration consists of two parts. First, we will deduce a family of critical systems consisting of nonlinear ordinary differential equations, indexed by the exponent p ∈ (1, ∞) of the Lebesgue spaces concerned. These systems can be used to obtain the optimal lower or upper bounds for eigenvalue gaps of Sturm–Liouville operators and are equivalent to non-convex Hamiltonian systems of two degrees of freedom. Second, with appropriate choices of exponents p, the critical systems are polynomial systems in four dimensions. These systems will be investigated from two aspects. The first one is that by applying the canonical transformation and the Darboux polynomial, we obtain the necessary and sufficient conditions for polynomial integrability of these polynomial critical systems. As a special example, we conclude that the system with p = 2 is polynomial completely integrable in the sense of Liouville. The second is that the linear stability of isolated singular points is characterized. By performing the Poincaré cross section technique, we observe that the systems have very rich dynamical behaviors, including periodic trajectories, quasi-periodic trajectories, and chaos.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89948914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Generalized conditional symmetries and pre-Hamiltonian operators 广义条件对称与前哈密顿算子

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-09-01 DOI: 10.1063/5.0147484

Bao Wang

引用次数: 0

Monotone complexity measures of multidimensional quantum systems with central potentials 具有中心势的多维量子系统的单调复杂性测度

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-09-01 DOI: 10.1063/5.0153747

J. S. Dehesa

引用次数: 0

Continuity of attractors for singularly perturbed semilinear problems with nonlinear boundary conditions and large diffusion 具有非线性边界条件和大扩散的奇摄动半线性问题吸引子的连续性

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-09-01 DOI: 10.1063/5.0151898

L. Pires, R. Samprogna

引用次数: 0

Response to “Comments on ‘Thermal solitons along wires with flux-limited lateral exchange’” [J. Math. Phys. 64, 094101 (2023)] 对“具有限通量横向交换的导线沿线热孤子”的评论[J]。数学。物理学报，64,094101 (2023)]

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-09-01 DOI: 10.1063/5.0170776

M. Sciacca, F. X. Alvarez, D. Jou, J. Bafaluy

引用次数: 0

Comments on “Thermal solitons along wires with flux-limited lateral exchange” [J. Math. Phys. 62, 101503 (2021)] 对“具有限通量横向交换的导线沿线热孤子”的评论[J]。数学。物理学报，62,101503 (2021)]

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-09-01 DOI: 10.1063/5.0157030

P. M. Jordan

引用次数: 0

Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble 与摄动高斯酉系综相关的painlevevv和合流Heun方程

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-08-01 DOI: 10.1063/5.0141161

Jianduo Yu, Siqi Chen, Chuanzhong Li, Mengkun Zhu, Yang Chen

{"title":"Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble","authors":"Jianduo Yu, Siqi Chen, Chuanzhong Li, Mengkun Zhu, Yang Chen","doi":"10.1063/5.0141161","DOIUrl":"https://doi.org/10.1063/5.0141161","url":null,"abstract":"We discuss the monic polynomials of degree n orthogonal with respect to the perturbed Gaussian weight w(z,t)=|z|α(z2+t)λe−z2,z∈R,t>0,α>−1,λ>0, which arises from a symmetrization of a semi-classical Laguerre weight wLag(z,t)=zγ(z+t)ρe−z,z∈R+,t>0,γ>−1,ρ>0. The weight wLag(z) has been widely investigated in multiple-input multi-output antenna wireless communication systems in information theory. Based on the ladder operator method, two auxiliary quantities, Rn(t) and rn(t), which are related to the three-term recurrence coefficients βn(t), are defined, and we show that they satisfy coupled Riccati equations. This turns to be a particular Painlevé V (PV, for short), i.e., PVλ22,−(1−(−1)nα)28,−2n+α+2λ+12,−12. We also consider the quantity σn(t)≔2tddtlnDn(t), which is allied to the logarithmic derivative of the Hankel determinant Dn(t). The difference and differential equations satisfied by σn(t), as well as an alternative integral representation of Dn(t), are obtained. The asymptotics of the Hankel determinant under a suitable double scaling, i.e., n → ∞ and t → 0 such that s ≔ 4nt is fixed, are established. Finally, by using the second order difference equation satisfied by the recurrence coefficients, we obtain the large n full asymptotic expansions of βn(t) with the aid of Dyson’s Coulomb fluid approach. By employing these results, the second differential equations satisfied by the orthogonal polynomials will be reduced to a confluent Heun equation.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"49 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86559781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analog of a Laplace–Runge–Lenz vector for particle orbits (time-like geodesics) in Schwarzschild spacetime 史瓦西时空中粒子轨道(类时测地线)的拉普拉斯-龙格-伦茨矢量的模拟

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-08-01 DOI: 10.1063/5.0147666

S. Anco, Jordan A. Fazio

{"title":"Analog of a Laplace–Runge–Lenz vector for particle orbits (time-like geodesics) in Schwarzschild spacetime","authors":"S. Anco, Jordan A. Fazio","doi":"10.1063/5.0147666","DOIUrl":"https://doi.org/10.1063/5.0147666","url":null,"abstract":"In Schwarzschild spacetime, time-like geodesic equations, which define particle orbits, have a well-known formulation as a dynamical system in coordinates adapted to the time-like hypersurface containing the geodesic. For equatorial geodesics, the resulting dynamical system is shown to possess a conserved angular quantity and two conserved temporal quantities, whose properties and physical meaning are analogs of the conserved Laplace–Runge–Lenz vector, and its variant known as Hamilton’s vector, in Newtonian gravity. When a particle orbit is projected into the spatial equatorial plane, the angular quantity yields the coordinate angle at which the orbit has either a turning point (where the radial velocity is zero) or a centripetal point (where the radial acceleration is zero). This is the same property as the angle of the respective Laplace–Runge–Lenz and Hamilton vectors in the plane of motion in Newtonian gravity. The temporal quantities yield the coordinate time and the proper time at which those points are reached on the orbit. In general, for orbits that have a single turning point, the three quantities are globally constant, and for orbits that possess more than one turning point, the temporal quantities are just locally constant as they jump at every successive turning point, while the angular quantity similarly jumps only if an orbit is precessing. This is analogous to the properties of a generalized Laplace–Runge–Lenz vector and generalized Hamilton vector which are known to exist for precessing orbits in post-Newtonian gravity. The angular conserved quantity is used to define a direct analog of these vectors at spatial infinity.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"57 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90664005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Global strong solutions for the multi-dimensional compressible viscoelastic flows with general pressure law 具有一般压力律的多维可压缩粘弹性流的全局强解

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-08-01 DOI: 10.1063/5.0158057

Yu Liu, Song Meng, Jiayan Wu, Ting Zhang

引用次数: 0

A singular linear statistic for a perturbed LUE and the Hankel matrices 扰动LUE和汉克尔矩阵的奇异线性统计量

IF 0.5 4区数学

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-08-01 DOI: 10.1063/5.0143858

Dan Wang, Mengkun Zhu, Yang Chen

引用次数: 0