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A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen 完全导电屏中平面孔径的电磁衍射的严格理论
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-15 DOI: 10.1063/5.0179521
Ying Liang, Hai Zhang
{"title":"A rigorous theory on electromagnetic diffraction by a planar aperture in a perfectly conducting screen","authors":"Ying Liang, Hai Zhang","doi":"10.1063/5.0179521","DOIUrl":"https://doi.org/10.1063/5.0179521","url":null,"abstract":"In this paper, we revisit the classic problem of diffraction of electromagnetic waves by an aperture in a perfectly conducting plane. We formulate the diffraction problem using a boundary integral equation that is defined on the aperture using Dyadic Green’s function. This integral equation turns out to align with the one derived by Bethe using fictitious magnetic charges and currents. We then investigate the boundary integral equation using a saddle point formulation and establish the well-posedness of the boundary integral equation, including the existence and uniqueness of the solution in an appropriately defined Sobolev space.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719687","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
Characterizing the geometry of the Kirkwood–Dirac-positive states 确定柯克伍德-迪拉克正态的几何特征
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-10 DOI: 10.1063/5.0164672
C. Langrenez, D. R. M. Arvidsson-Shukur, S. De Bièvre
{"title":"Characterizing the geometry of the Kirkwood–Dirac-positive states","authors":"C. Langrenez, D. R. M. Arvidsson-Shukur, S. De Bièvre","doi":"10.1063/5.0164672","DOIUrl":"https://doi.org/10.1063/5.0164672","url":null,"abstract":"The Kirkwood–Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables A and B. KD distributions behave similarly to classical joint probability distributions but can assume negative and nonreal values. In recent years, KD distributions have proven instrumental in mapping out nonclassical phenomena and quantum advantages. These quantum features have been connected to nonpositive entries of KD distributions. Consequently, it is important to understand the geometry of the KD-positive and -nonpositive states. Until now, there has been no thorough analysis of the KD positivity of mixed states. Here, we investigate the dependence of the full convex set of states with positive KD distributions on the eigenbases of A and B and on the dimension d of the Hilbert space. In particular, we identify three regimes where convex combinations of the eigenprojectors of A and B constitute the only KD-positive states: (i) any system in dimension 2; (ii) an open and dense probability one set of bases in dimension d = 3; and (iii) the discrete-Fourier-transform bases in prime dimension. Finally, we show that, if for example d = 2m, there exist, for suitable choices of A and B, mixed KD-positive states that cannot be written as convex combinations of pure KD-positive states. We further explicitly construct such states for a spin-1 system.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141588322","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
The steady Prandtl boundary layer expansions for non-shear Euler flow 非剪切欧拉流的稳定普朗特边界层扩展
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-10 DOI: 10.1063/5.0192671
Chen Gao, Liqun Zhang
{"title":"The steady Prandtl boundary layer expansions for non-shear Euler flow","authors":"Chen Gao, Liqun Zhang","doi":"10.1063/5.0192671","DOIUrl":"https://doi.org/10.1063/5.0192671","url":null,"abstract":"We continue the study on the validity of the Prandtl boundary layer expansions in [Gao et al., Sci. China Math. 66, 679–722 (2023)], whereby estimating the stream-function of the remainder, we proved the case when the Euler flow is the perturbation of shear flow in a narrow domain. In this paper, we obtain a new derivatives estimate of stream-function away from the boundary layer and then prove the validity of expansions for any non-shear Euler flow, provided that the width of the domain is small.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141586151","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
Ground state energy of Bogoliubov energy functional in the high density limit 高密度极限下波哥留波夫能量函数的基态能量
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-09 DOI: 10.1063/5.0206192
Norbert Mokrzański, Bartosz Pałuba
{"title":"Ground state energy of Bogoliubov energy functional in the high density limit","authors":"Norbert Mokrzański, Bartosz Pałuba","doi":"10.1063/5.0206192","DOIUrl":"https://doi.org/10.1063/5.0206192","url":null,"abstract":"We consider the Bogoliubov energy functional proposed by Napiórkowski, Reuvers and Solovej and analize it in the high density regime. We derive a two term asymptotic expansion of the ground state energy.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141575227","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 Mathieu conjecture for Sp(N) and G2 关于 Sp(N) 和 G2 的马蒂厄猜想
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-08 DOI: 10.1063/5.0206983
Kevin Zwart
{"title":"On the Mathieu conjecture for Sp(N) and G2","authors":"Kevin Zwart","doi":"10.1063/5.0206983","DOIUrl":"https://doi.org/10.1063/5.0206983","url":null,"abstract":"As a direct continuation of Zwart [J. Math. Phys. 64(10), 101701 (2023)], which is built on the work of Müger and Tuset [Indagationes Math. 35(1), 114 (2024)], we reduce the Mathieu conjecture, formulated by Mathieu [Algèbra Non Commutative, Groupes Quantiques et Invariants, edited by Alex, J. and Cauchon, G. (Société Mathématique de France, Reims, 1997), Vol. 2, pp. 263–279], for Sp(N) and G2 to a conjecture involving functions over Rn×(S1)m with n,m∈N0. The proofs rely on Euler-style parametrizations of these groups, a specific version of the KAK decomposition, which we discuss and prove.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141575228","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
Some spectral comparison results on infinite quantum graphs 无限量子图的一些谱比较结果
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-02 DOI: 10.1063/5.0178226
P. Bifulco, J. Kerner
{"title":"Some spectral comparison results on infinite quantum graphs","authors":"P. Bifulco, J. Kerner","doi":"10.1063/5.0178226","DOIUrl":"https://doi.org/10.1063/5.0178226","url":null,"abstract":"In this paper we establish spectral comparison results for Schrödinger operators on a certain class of infinite quantum graphs, using recent results obtained in the finite setting. We also show that new features do appear on infinite quantum graphs such as a modified local Weyl law. In this sense, we regard this paper as a starting point for a more thorough investigation of spectral comparison results on more general infinite metric graphs.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528538","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
The singular limits of the Riemann solutions as pressure vanishes for a reduced two-phase mixtures model with non-isentropic gas state 具有非各向同性气体状态的两相混合物模型在压力消失时的黎曼解奇异极限
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-02 DOI: 10.1063/5.0191801
W. Jiang, D. Jin, T. Li, T. Chen
{"title":"The singular limits of the Riemann solutions as pressure vanishes for a reduced two-phase mixtures model with non-isentropic gas state","authors":"W. Jiang, D. Jin, T. Li, T. Chen","doi":"10.1063/5.0191801","DOIUrl":"https://doi.org/10.1063/5.0191801","url":null,"abstract":"We study the cavitation and concentration phenomena of the Riemann solutions for a reduced two-phase mixtures model with non-isentropic gas state in vanishing pressure limit. We solve the Riemann problem by constructing the regions in (p, u, s) coordinate system. Then we obtain the limiting behaviors of the Riemann solutions and the formation of δ-shock waves and vacuum as pressure vanishes. We conclude that, as pressure vanishes, the limit of Riemann solutions is the Riemann solutions of the reduced 2-dimensional pressureless gas dynamics model. Finally, we present numerical simulations which are consistent with our theoretical analysis.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528539","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
Herglotz-type vakonomic dynamics and its Noether symmetry for nonholonomic constrained systems 赫格洛茨型自旋动力学及其非自旋约束系统的诺特对称性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-02 DOI: 10.1063/5.0157564
Li-Qin Huang, Yi Zhang
{"title":"Herglotz-type vakonomic dynamics and its Noether symmetry for nonholonomic constrained systems","authors":"Li-Qin Huang, Yi Zhang","doi":"10.1063/5.0157564","DOIUrl":"https://doi.org/10.1063/5.0157564","url":null,"abstract":"In this paper, Herglotz-type vakonomic dynamics and Noether theory of nonholonomic systems are studied. Firstly, Herglotz-type vakonomic dynamical equations for nonholonomic systems are derived on the premise of Herglotz variational principle. Secondly, in terms of the Herglotz-type vakonomic dynamical equations, the Noether symmetry of Herglotz-type vakonomic dynamics is explored, and the Herglotz-type vakonomic dynamical Noether theorems and their inverse theorems are deduced. Finally, the conservation laws of Appell–Hamel case with non-conservative forces are analyzed to show the validity of our results.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528540","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 lattice hexagonal crystallization for non-monotone potentials 关于非单调势的晶格六方结晶
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-01 DOI: 10.1063/5.0200485
Senping Luo, Juncheng Wei
{"title":"On lattice hexagonal crystallization for non-monotone potentials","authors":"Senping Luo, Juncheng Wei","doi":"10.1063/5.0200485","DOIUrl":"https://doi.org/10.1063/5.0200485","url":null,"abstract":"We prove that for α ≥ 1, among 2d unit density lattices, minL∑P∈L(|P|2−β)e−πα|P|2 is achieved at hexagonal lattice for β≤12πα and does not exist for β>12πα. Here the hexagonal lattice with unit density can be expressed by Λ1=132[Z(1,0)⊕Z(12,32)]. This leads to two applications as follows. (1) Assume that α ≥ 1. Then, among 2d unit density lattices, minL∑P∈L|P|2e−πα|P|2 is achieved at hexagonal lattice. (2) Assume that β > α ≥ 1. Then minz∈Hθ(α;z)−bθ(β;z) is achieved at z=eiπ3 (corresponding to hexagonal lattice) for b≤βα and does not exist for b>βα. Here θ(α; z) is the two-dimensional Theta function.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509063","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
Floquet isospectrality of the zero potential for discrete periodic Schrödinger operators 离散周期薛定谔算子零势的 Floquet 等谱性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-01 DOI: 10.1063/5.0201744
Matthew Faust, Wencai Liu, Rodrigo Matos, Jenna Plute, Jonah Robinson, Yichen Tao, Ethan Tran, Cindy Zhuang
{"title":"Floquet isospectrality of the zero potential for discrete periodic Schrödinger operators","authors":"Matthew Faust, Wencai Liu, Rodrigo Matos, Jenna Plute, Jonah Robinson, Yichen Tao, Ethan Tran, Cindy Zhuang","doi":"10.1063/5.0201744","DOIUrl":"https://doi.org/10.1063/5.0201744","url":null,"abstract":"Let Γ=q1Z⊕q2Z⊕⋯⊕qdZ, with qj∈Z+ for each j ∈ {1, …, d}, and denote by Δ the discrete Laplacian on ℓ2Zd. Using Macaulay2, we first numerically find complex-valued Γ-periodic potentials V:Zd→C such that the operators Δ + V and Δ are Floquet isospectral. We then use combinatorial methods to validate these numerical solutions.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528542","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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