Journal of Mathematical Physics最新文献

Topological recursion of the Weil–Petersson volumes of hyperbolic surfaces with tight boundaries 具有紧密边界的双曲面的魏尔-彼得森体积的拓扑递归

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-11 DOI: 10.1063/5.0192711

Timothy Budd, Bart Zonneveld

{"title":"Topological recursion of the Weil–Petersson volumes of hyperbolic surfaces with tight boundaries","authors":"Timothy Budd, Bart Zonneveld","doi":"10.1063/5.0192711","DOIUrl":"https://doi.org/10.1063/5.0192711","url":null,"abstract":"The Weil–Petersson volumes of moduli spaces of hyperbolic surfaces with geodesic boundaries are known to be given by polynomials in the boundary lengths. These polynomials satisfy Mirzakhani’s recursion formula, which fits into the general framework of topological recursion. We generalize the recursion to hyperbolic surfaces with any number of special geodesic boundaries that are required to be tight. A special boundary is tight if it has minimal length among all curves that separate it from the other special boundaries. The Weil–Petersson volume of this restricted family of hyperbolic surfaces is shown again to be polynomial in the boundary lengths. This remains true when we allow conical defects in the surface with cone angles in (0, π) in addition to geodesic boundaries. Moreover, the generating function of Weil–Petersson volumes with fixed genus and a fixed number of special boundaries is polynomial as well, and satisfies a topological recursion that generalizes Mirzakhani’s formula. This work is largely inspired by recent works by Bouttier, Guitter, and Miermont [Ann. Henri Lebesgue 5, 1035–1110 (2022)] on the enumeration of planar maps with tight boundaries. Our proof relies on the equivalence of Mirzakhani’s recursion formula to a sequence of partial differential equations (known as the Virasoro constraints) on the generating function of intersection numbers. Finally, we discuss a connection with Jackiw–Teitelboim (JT) gravity. We show that the multi-boundary correlators of JT gravity with defects are expressible in the tight Weil–Petersson volume generating functions, using a tight generalization of the JT trumpet partition function.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226329","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

Rescaling transformations and the Grothendieck bound formalism in a single quantum system 单量子系统中的重定标变换和格罗内狄克约束形式主义

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-11 DOI: 10.1063/5.0201690

A. Vourdas

{"title":"Rescaling transformations and the Grothendieck bound formalism in a single quantum system","authors":"A. Vourdas","doi":"10.1063/5.0201690","DOIUrl":"https://doi.org/10.1063/5.0201690","url":null,"abstract":"The Grothedieck bound formalism is studied using “rescaling transformations,” in the context of a single quantum system. The rescaling transformations enlarge the set of unitary transformations (which apply to isolated systems), with transformations that change not only the phase but also the absolute value of the wavefunction, and can be linked to irreversible phenomena (e.g., quantum tunneling, damping and amplification, etc). A special case of rescaling transformations are the dequantisation transformations, which map a Hilbert space formalism into a formalism of scalars. The Grothendieck formalism considers a “classical” quadratic form C(θ) which takes values less than 1, and the corresponding “quantum” quadratic form Q(θ) which takes values greater than 1, up to the complex Grothendieck constant kG. It is shown that Q(θ) can be expressed as the trace of the product of θ with two rescaling matrices, and C(θ) can be expressed as the trace of the product of θ with two dequantisation matrices. Values of Q(θ) in the “ultra-quantum” region (1, kG) are very important, because this region is classically forbidden [C(θ) cannot take values in it]. An example with Q(θ)∈(1,kG) is given, which is related to phenomena where classically isolated by high potentials regions of space, communicate through quantum tunneling. Other examples show that “ultra-quantumness” according to the Grothendieck formalism (Q(θ)∈(1,kG)), is different from quantumness according to other criteria (like quantum interference or the uncertainty principle).","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207490","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

Integrable decompositions for the (2 + 1)-dimensional multi-component Ablowitz–Kaup–Newell–Segur hierarchy and their applications (2 + 1)维多分量阿布洛维茨-考普-纽维尔-塞古尔层次结构的积分分解及其应用

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-11 DOI: 10.1063/5.0203907

Xiaoming Zhu, Shiqing Mi

{"title":"Integrable decompositions for the (2 + 1)-dimensional multi-component Ablowitz–Kaup–Newell–Segur hierarchy and their applications","authors":"Xiaoming Zhu, Shiqing Mi","doi":"10.1063/5.0203907","DOIUrl":"https://doi.org/10.1063/5.0203907","url":null,"abstract":"This paper investigates integrable decompositions of the (2 + 1)-dimensional multi-component Ablowitz-Kaup-Newell-Segur (AKNS in brief) hierarchy. By utilizing recursive relations and symmetric reductions, it is demonstrated that the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional coupled multi-component AKNS hierarchy can be decomposed into the corresponding n1-flow and n2-flow of the coupled multi-component AKNS hierarchy. Specifically, except for two specific scenarios, the (n2 − n1 + 1)-flow of the (2 + 1)-dimensional reduced multi-component AKNS hierarchy can similarly be decomposed into the corresponding n1-flow and n2-flow of the reduced multi-component AKNS hierarchy. Through the application of these integrable decompositions and Darboux transformation techniques, multiple solitons for the standard focusing multi-component “breaking soliton” equations, as well as singular, exponential, and rational solitons for the nonlocal defocusing multi-component “breaking soliton” equations, are systematically presented. Furthermore, the elastic interactions and dynamical behaviors among these soliton solutions are thoroughly investigated without loss of generality.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207492","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

Solutions for a flame propagation model in porous media based on Hamiltonian and regular perturbation methods 基于哈密顿法和正则扰动法的多孔介质中火焰传播模型的解决方案

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-10 DOI: 10.1063/5.0149573

Saeed ur Rahman, José Luis Díaz Palencia

引用次数: 0

A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces 具有近似磁通量面的等离子体中非线性磁场湍流的简化理想 MHD 系统

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-10 DOI: 10.1063/5.0186445

Naoki Sato, Michio Yamada

{"title":"A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces","authors":"Naoki Sato, Michio Yamada","doi":"10.1063/5.0186445","DOIUrl":"https://doi.org/10.1063/5.0186445","url":null,"abstract":"This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal Magnetohydrodynamics (MHD) configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that is relevant for plasma confinement in stellarators. The aim is to gather insight on magnetic field dynamics, to elucidate accessibility and stability of three-dimensional MHD equilibria, as well as to formulate practical methods to compute them. Starting from the ideal MHD equations, a reduced dynamical system of two coupled nonlinear partial differential equations for the flux function and the angle variable associated with the Clebsch representation of the magnetic field is obtained. It is shown that under suitable boundary and gauge conditions such reduced system preserves magnetic energy, magnetic helicity, and total magnetic flux. The noncanonical Hamiltonian structure of the reduced system is identified, and used to show the nonlinear stability of steady solutions against perturbations involving only one Clebsch potential. The Hamiltonian structure is also applied to construct a dissipative dynamical system through the method of double brackets. This dissipative system enables the computation of MHD equilibria by minimizing energy until a critical point of the Hamiltonian is reached. Finally, an iterative scheme based on the alternate solution of the two steady equations in the reduced system is proposed as a further method to compute MHD equilibria. A theorem is proven which states that the iterative scheme converges to a nontrivial MHD equilbrium as long as solutions exist at each step of the iteration.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207491","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

Viscosity solutions to a Cauchy type problem for timelike Lorentzian eikonal equation 时间类洛伦兹埃克纳方程的考奇类问题的粘度解

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-10 DOI: 10.1063/5.0178336

Siyao Zhu, Xiaojun Cui, Tianqi Shi

引用次数: 0

Stückelberg-modified massive Abelian 3-form theory: Constraint analysis, conserved charges and BRST algebra 经 Stückelberg 修正的大质量阿贝尔 3 形理论：约束分析、守恒电荷和 BRST 代数

IF 1.3 3区物理与天体物理

Journal of Mathematical Physics Pub Date : 2024-09-09 DOI: 10.1063/5.0205593

A. K. Rao, R. P. Malik

{"title":"Stückelberg-modified massive Abelian 3-form theory: Constraint analysis, conserved charges and BRST algebra","authors":"A. K. Rao, R. P. Malik","doi":"10.1063/5.0205593","DOIUrl":"https://doi.org/10.1063/5.0205593","url":null,"abstract":"For the Stückelberg-modified massive Abelian 3-form theory in any arbitrary D-dimension of spacetime, we show that its classical gauge symmetry transformations are generated by the first-class constraints. We establish that the Noether conserved charge (corresponding to the local gauge symmetry transformations) is same as the standard form of the generator for the underlying local gauge symmetry transformations (expressed in terms of the first-class constraints). We promote these classical local, continuous and infinitesimal gauge symmetry transformations to their quantum counterparts Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations which are respected by the coupled (but equivalent) Lagrangian densities. We derive the conserved (anti-)BRST charges by exploiting the theoretical potential of Noether’s theorem. However, these charges turn out to be non-nilpotent. Some of the highlights of our present investigation are (i) the derivation of the off-shell nilpotent versions of the (anti-)BRST charges from the standard non-nilpotent Noether conserved (anti-)BRST charges, (ii) the appearance of the operator forms of the first-class constraints at the quantum level through the physicality criteria with respect to the nilpotent versions of the (anti-)BRST charges, and (iii) the deduction of the Curci–Ferrari-type restrictions from the straightforward equality of the coupled (anti-)BRST invariant Lagrangian densities as well as from the requirement of the absolute anticommutativity of the off-shell nilpotent versions of the conserved (anti-)BRST charges.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142207493","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 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":null,"pages":null},"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

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

引用次数: 0